The starting salaries of individuals with an undergraduate degree from UC Riverside are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000?

Answer:

The probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000 is 0.7699.

Step-by-step explanation:

Let X denote the starting salaries of individuals with an undergraduate degree from UC Riverside.

It is provided that, [tex]X\sim N(\$40,000,\ \$5,000^{2})[/tex]

Compute the value of P (34000 < X < 46000) as follows:

[tex]P (34000 < X < 46000)=P(\frac{34000-40000}{5000}<\frac{X-\mu}{\sigma}<\frac{46000-40000}{5000})\\\\=P(-1.2<Z<1.2)\\\\=P(Z<1.2)-P(Z<-1.2)\\\\=0.88493-0.11507\\\\=0.76986\\\\\approx 0.7699[/tex]

Thus, the probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000 is 0.7699.

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