Question

Suppose the age is normally distributed with a mean of 62 years old and a standard deviation of 3.7 years. 1. One of the patient’s age of diagnosis was 1.63 standard deviations above the mean. What was this patient’s age when he was diagnosed? 2.Using Z > 2 as a criterion for an outlier, what is the minimum sample size such that a sample mean of 62.5 years would be classified as an outlier?

Answer 1

Result:

Suppose the age is normally distributed with a mean of 62 years old and a standard deviation of 3.7 years. 1. One of the patient’s age of diagnosis was 1.63 standard deviations above the mean. What was this patient’s age when he was diagnosed?

x = mean+z*sd

given z value is 1.63

The required age = 62+1.63*3.7

=68.031

2.Using Z > 2 as a criterion for an outlier, what is the minimum sample size such that a sample mean of 62.5 years would be classified as an outlier?

We have to find n such that

2 < (62.5-62)/3.7/sqrt(n)

3.7/sqrt(n) < (62.5-62)/2 =0.25

Sqrt(n) > 3.7/0.25 =14.8

n > 219.04

We need 220 as minimum sample size such that a sample mean of 62.5 years would be classified as an outlier.