In a population of children at a local elementary school, the average number of sick days taken per year is 6 with a standard deviation of 3. Assume that this distribution is normal. For random samples of size 125, what is the probability that a sample mean for sick days would be 7 or greater?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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In a population of children at a local elementary school, the average number of sick days taken per year is 6 with a standard deviation of 3. Assume that this distribution is normal. For random samples of size 125, what is the probability that a sample mean for sick days would be 7 or greater?

 

!!!Can you please show the formula Used!!!

Expert Solution
Step 1

To calculate the required probability we need to the score 7 in to z-score then we will use z-table to calculate the probability.

Statistics homework question answer, step 1, image 1

 

Step 2

The Required formula to calculate the Z score is,

Statistics homework question answer, step 2, image 1

Statistics homework question answer, step 2, image 2

 

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,