Question

1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Calculate the Z score associated with 3 siblings. Your answer should be rounded to two decimal places, like 5.43 or 1.30.

2. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Using the standard normal table, calculate the proportion of respondents who had more than 2 siblings. Your answer should be rounded to two decimal places, like 0.43 or 0.30.

Answer 1

-0.24 ; 0.71

Explanation:

Given that :

Mean number of siblings (m) = 3.76

Standard deviation (s) = 3.18

Z score associated with 3 siblings

x = 3

Using the relation :

Zscore = (x - m) / s

Zscore = (3 - 3.76) / 3.18

Zscore = - 0.76 / 3.18

Zscore = −0.238993

Zscore = - 0.24

2.) proportion of respondents with more than 2 siblings

Using the z probability calculator :

X > 2

Obtain the standardized score :

Zscore = (x - m) / s

Zscore = (2 - 3.76) / 3.18

Zscore = - 1.76 / 3.18

Zscore = −0.5534591

Zscore = - 0.55

Using the z table :

P(Z ≥ - 0.55) = 1 - p(Z ≤ - 0.55) ; p(Z ≤ - 0.55) = 0.2912

1 - p(Z ≤ - 0.55) = 1 - 0.2912 = 0.7088 = 0.71