Question

In: Statistics and Probability

ABC Corporation has 350 employees. The distribution of number of sick days per employee per year...

  1. ABC Corporation has 350 employees. The distribution of number of sick days per employee per year for the population of 350 employees is not highly skewed and has a mean of 12 and a standard deviation of 4. Suppose a simple random sample of 25 employees' number of sick days is taken, what is the probability that the sample of 25 will have mean number of sick days between 10 and 14? Show your work.

Solutions

Expert Solution

Solution :

Given that,

mean = = 12

standard deviation = = 4

n = 25

=   = 12

= / n = 4 / 25 = 0.8

P(10 < < 14) = P((10 - 12) / 0.8<( - ) / < (14 - 12) / 0.8))

= P(-2.5 < Z < 2.5)

= P(Z < 2.5) - P(Z < -2.5) Using standard normal table,  

= 0.9938 - 0.0062

= 0.9876

Probability = 0.9876  

orchestra answered 2 years ago
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