Suppose the owner of a local apple orchard has 4 half-bushels of apples to sell. He loads them on his truck, and drives his route, stopping at stores along the way attempting to sells the apples. Suppose:

- Each half-bushel is sold for $40.

- It will cost $15 of gas to drive the route.

Historically, the orchard owner knows he will have a 40% chance of making no sales, a 30% chance of selling 1 half-bushel, a 10% chance of selling 2 half-bushels, and a 10% chance of selling 3 half-bushels.

(a) Calculate the orchard owner’s expected profit from driving the route.

(b) Calculate the standard deviation of the profit from driving the route.

Answers

Answer 1

Answer:

a) The orchard owner's expected profit from driving the route is $33.

b) The standard deviation of the profit is $27.28

Step-by-step explanation:

a) Data and Calculations:

Apples to sell = 4 half-bushels

Price of each half-bushel sold = $40

Sales revenue = $160 ($40 *4)

Cost of driving the route = $15

Expected values:

Event                          Probability  Revenue       Profit         Expected  Profit

No Sales                        40%            $0         ($15) ($0 - $15)        ($6.00)

Selling 1 half-bushel      30%         $40         $25 ($40 - $15)         $7.50

Selling 2 half-bushels   10%          $80         $65 ($80 - $15)        $6.50

Selling 3 half-bushels   10%         $120       $105 ($120 - $15)     $10.50

Selling 4 half-bushels   10%         $160       $145 ($160 - $15)     $14.50

Total expected profit = $33

Event                          Expected  Profit  Mean        Squared

                                                                       Difference

No Sales                            ($6.00)        -39             1,521

Selling 1 half-bushel           $7.50         -25.5           650.25

Selling 2 half-bushels        $6.50         -26.5           702.25

Selling 3 half-bushels      $10.50         -22.50         506.25

Selling 4 half-bushels      $14.50         -18.50          342.25

Sum of squared differences                                     3,722

Mean of squared differences = 744.4 (3,722/5)

Standard deviation = square root of the mean

= 27.28

= $27.28


Related Questions

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Answers

Answer:

1 and 1/3

Step-by-step explanation:

The absolute value means that you have a positive sign no matter what the value is. It is the distance in units from 0 on the number line to the point in question.

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Answer:

4

Step-by-step explanation:

Answer:

119.6

Step-by-step explanation:

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Julie is trying to choose between two packs of cookies. Pack A has 36 cookies for $5.90. Pack B has 24 cookies for $4.10. Which pack has cheaper cookies

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Answer:

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Step-by-step explanation:

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Answers

Answer:

No

Step-by-step explanation:

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Answers

Answer:

A B and D

Step-by-step explanation:

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y = -4x – 5
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Is (3, 7) a solution of the system?

Answers

Answer:

no

Step-by-step explanation:

this is because

-12-5=-17

-28-2= -30

Nebi has already typed 250 words. He then starts a timer and finds that he types 150 words in 3 minutes. If nebi types at a constant rate, write a linear equation to represent the number of words w that nebi types m minutes after starting the timer

Answers

Answer:

[tex]w=250+50m[/tex]

Step-by-step explanation:

Number words Nebi has typed = 250

t = Duration of typing = 3 minutes

Number of words typed in 3 minutes = 150

Rate of typing in 3 minutes

[tex]\dfrac{150}{3}=50\ \text{words/minute}[/tex]

So the linear equation representing the situation would be

[tex]w=250+50m[/tex]

Where

w = Number of words

m = Number of minutes after starting the timer

The linear equation to represent the number of words w that nebi types m minutes after starting the timer is w = 250 + 50m

Given:

Words already typed = 250 words.

Words typed in 3 minutes = 150 words

Words typed per minute = 150 words / 3 minutes

= 50 words per minute

w = Total words typed

m = number of minutes

The equation:

Total words typed = Words already typed + (Words typed per minute × number of minutes )

w = 250 + (50 × m)

w = 250 + 50m

Therefore, linear equation to represent the number of words w that nebi types m minutes after starting the timer is w = 250 + 50m

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In San Diego, the weather was sunny 90% of the says this past June. How many days was it sunny​

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Answer:

27 days

Step-by-step explanation:

June has 30 days, So our equation looks like this:

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what is an equation for the translation of y=|x| left 7 units?

Answers

Answer:

y=|x+7|

Step-by-step explanation:

to move an absolute value equation to the left, all you have to do is add 7 to the inside of the absolute value:

y=|x+7|

We can check that this works, because the x-intercept moved from (0, 0) to (0, -7), meaning that the whole graph got translated 7 units to the left.

simplify 6³÷2³×9^-2​

Answers

answer is

0.33333333333

plz help me
is 7/3 less than 6 ​

Answers

Answer:

yes

Step-by-step explanation:

I figured this out by determining how many times 3 fits into 7.

7/3 is equal to 2 and 1/3

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Hope this helps <3

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Answers

Answer:

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Step-by-step explanation:

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C=2πr

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Pi is [tex]3.14[/tex]...

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A preschool class has 9 girls and 11 boys in
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Answers

Answer:

45%

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Answer:

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Step-by-step explanation:

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from Khan academy

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2 is the answer djeidiejdieoeoododos

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Answers

Answer:

the factors of prime numbers are only 1 and itself

Answer:

A factor number can only be divided by itself or 1 meaning it cant be a factor anything more than that.

Step-by-step explanation:

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Pls help

Answers

Answer:

The first thing you do is make the denominators equal on both sides.

Step-by-step explanation:

As a example if you have the equation:

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you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10

this would make the equation

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next you have to do the same with the numerator.

so sence you multiplied the [tex]\frac{1}{2}[/tex] by five you will get [tex]\frac{5}{10}[/tex]

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Answer:

3 simple steps

Step-by-step explanation:

1.     Make sure the bottom numbers ( the denominators ) are the same

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Answers

Answer:

p/4

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Answer:

p/4

Step-by-step explanation:

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At Nivea's Newsstand, 6 magazines cost $12.00. How many magazines could you buy with $16.00?

Answers

Answer:

You could by 8 magazines

Step-by-step explanation:

First, set up the equation 6/12=x/16

cross multiple to get 12x=96

divide both sides by 12 and x = 8

This is a fun, but simple unit rate problem! We are solving for x.

Divide 12 by 6 (cost is usually always first when dividing for unit rate). You’ll get 2.

That means, for every one magazine, it’s 2 dollars.

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Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability that one junior and one senior are chosen for the two positions?a. 0.395 b. 0.444 c. 0.506 d. 0569 e. 0.722

Answers

Answer:

The probability that one junior and one senior are chosen for the two positions is 0.556.

Step-by-step explanation:

The information provided is as follows:

Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly.

There are a total of 9 students who applied for the two open student council positions.

The total number of ways to select two students from 9 is: [tex]{9\choose 2}=\frac{9!}{(9-2)!}=36[/tex]

Compute the probability that one junior and one senior are chosen for the two positions as follows:

[tex]P(\text{1 Junior and 1 Senior})=\frac{5\times 4}{36}=0.556[/tex]

Thus, the probability that one junior and one senior are chosen for the two positions is 0.556.

If 200 men can make a road 5 km long in 25 days ,how much overtime per day must 60 men can work to finish an road 2 km in 32 days , 12 hours being a day's work ?​

Answers

Answer:

Solution with step by step explanation is the image attached below

A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What percent of the radios will function for more than 16 years? (b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X. (c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years? (d) If 10% of the radios will function for more than X years, find X.
Help, please!!

Answers

Answer:

(a) 5.48%

(b) 17.82 years

(c) 21.19%

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

Cross Multiply

2.326 × 2.5 = x - 12

5.815 = x - 12

x = 12 + 5.815

x = 17.815

Approximately = 17.82 years

(c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years?

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

Maria needs to be at the airport terminal at 15:20. It will take 2 hours to
drive to the airport from her home, and a further 30 minutes to park and get
to the terminal.
What is the latest time she should leave home?
Give
your answer as a time in the 24-hour clock.

Answers

Answer:

12:50

Step-by-step explanation:

15:20 - 2h= 13:20

13:20-30 min= 12:50

Answer:

12:50

Step-by-step explanation:

If it takes 2 hours to get there, you subtract 2 hours from 15:20 which gives you 13:20. It also says that she needs 30 minutes to park so you subtract that from 13:20 giving you 12:50

What is the amount earned by a car salesman if he sold a truck for $37.500 at a 2% commission? 15​

Answers

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