Question

In: Statistics and Probability

A normal distribution has a mean of 21 and a standard deviation of 3.2. What is...

A normal distribution has a mean of 21 and a standard deviation of 3.2. What is the Z-score for a sample with a value of 23? (calculate to 1 decimal)

The mean weight of your sample of 100 doves is 6.59 grams, with a standard deviation of 1.1. You look at one sample and its weight is 6.08 grams. What is the Z-score for this sampled dove? Please carry your answer to three decimal places.

Solutions

Expert Solution

Solution :

Given that ,

(a)

mean = = 21

standard deviation = = 3.2

x = 23

z = (x - ) / = (23 - 21) / 3.2 = 2 / 3.2 = 0.625

z - score = 0.625

(b)

mean = = 6.59

standard deviation = = 1.1

n = 100

= 6.08

= 6.59 and

= / n = 1.1 / 100 = 1.1 / 10 = 0.11

z = ( - ) / = (6.08 - 6.59) / 0.11 = -0.51 / 0.11 = -4.636

z score = -4.636


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