Question

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 1

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.

Explanation:

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

It is provided that,
`X\sim N(\$40,000,\ \$5,000^(2))`

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

`P (34000 < X < 46000)=P((34000-40000)/(5000)<(X-\mu)/(\sigma)<(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`

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.