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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