usiness Weekly conducted a survey of graduates from

celesteh12

celesteh12

Answered question

2022-10-13

usiness Weekly conducted a survey of graduates from several top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $172,000. Assume the standard deviation is $36,000. Suppose you take a simple random sample of 16 graduates. Round all answers to four decimal places if necessary.

 

  • What is the standard deviation of distribution of X
  • What is the standard deviation of X¯
  • For a single randomly selected graduate, find the probability that her salary is between $164,800 and $177,900. 
  • For a simple random sample of 16 graduates, find the probability that the average salary is between $164,800 and $177,900. 
  • For part d), is the assumption of normal necessary? No or Yes

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-29Added 184 answers

To solve this problem, let's first define the variables:
μ = Mean annual salary for graduates 10 years after graduation = 172,000
σ = Standard deviation of the population = 36,000
n = Sample size = 16
(a) Standard deviation of the distribution of X:
The standard deviation of the distribution of X, denoted as σX, can be calculated using the formula:
σX=σn
Substituting the given values, we have:
σX=36,00016
σX=36,0004
σX=9,000
Therefore, the standard deviation of the distribution of X is 9,000.
(b) Standard deviation of X:
The standard deviation of X, denoted as sX, is an estimate of the population standard deviation based on the sample. It can be calculated using the formula:
sX=σn
Substituting the given values, we have:
sX=36,00016
sX=36,0004
sX=9,000
Therefore, the standard deviation of X is also 9,000.

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