Question

The starting salary for a computer programmer major has a mean of $39,269 and a standard deviation of $2550. The probability that a randomly selected computer programmer major received a starting salary less than $38,000 is

Answer 1

Answer:

The probability that a randomly selected programmer major received a salary less than 38000 is 0,3085

Step-by-step explanation:

We will assume that the salaries are Normally distributed. Lets call X the salary of a random major programmer in dollars. We want the pprobability of X being less than 38000. For it, we will standarize X. Lets call W the standarization, given by the formula

$W = \frac{X-\mu}{\sigma}=\frac{X-39269}{2550}  $

Lets denote $\phi$ the cumulative distribution function of the standard normal variable W. The values of $\phi$ are well known and they can be found in the attached file. Now, lets calcualte the probability of X being less than 38000 using $\phi$

$P(X<38000) = P(\frac{X-39269}{2550} < \frac{38000-39269}{2550}) = P(W < -0.50)$

Since the density function of a standard normal random variable is symmetric, then $\phi(-0.50) = 1-\phi(0.50) = 1-0.6915 = 0.3085$

The probability that a randomly selected programmer major received a salary less than 38000 is 0,3085.

Answer 2

Answer:

The probability is 0.6915

Step-by-step explanation:

Test statistic (z) = (starting salary - mean starting salary)/standard deviation

starting salary = $38,000

mean starting salary = $39,269

standard deviation = $2,550

z = (38,000 - 39,269)/2550 = -1269/2550 = -0.50

The cumulative area of the test statistic is the probability that the starting salary is less than $38,000. The cumulative area is 0.6915.

Therefore, the probability is 0.6915.