Question

The average starting salary offer for marketing majors who graduated in 2007 was $39,269Assume that x, the starting salary for marketing majors in the class of '07, is normally distibuted with a mean of $39,269 and a standard deviation of $2,550The Probability that a randomly selected marketing major from the class of '07 received a starting salary offer greater than $41,950 is_____A. .1469B. .05C..8531D. .3531

Answer 1

Answer:

A. .1469

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 39269, \sigma = 2550$

The Probability that a randomly selected marketing major from the class of '07 received a starting salary offer greater than $41,950 is

This is 1 subtracted by the pvalue of Z when X = 41950. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41950 - 39269}{2550}$

$Z = 1.05$

$Z = 1.05$ has a pvalue of 0.8531

1 - 0.8531 = 0.1469

So the correct answer is:

A. .1469