Question

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 124000 dollars. Assume the standard deviation is 35000 dollars. Suppose you take a simple random sample of 52 graduates.

Find the probability that a single randomly selected salary is less than 128000 dollars. Answer = ?

Find the probability that a sample of size n=52 is randomly selected with a mean that is less than 128000 dollars. Answer = ?

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 124000

standard deviation = = 35000

a) P(x < 128000) = P[(x - ) / < (128000 - 124000) / 35000]

= P(z < 0.11 )

Using z table,

= 0.5438

b) n = 52

=   = 124000

= / n = 35000/ 52 = 4854

P( < 128000) = P(( - ) / < (128000 - 124000) / 4854)

= P(z < 0.82)

Using z table

=0.7939