Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 16. Determine the percent
age of samples of size 4 that will have mean scores within 12 points of the population mean score of 220. Round your answer to two decimal places.
1 answer:
Answer:
86.64%
Step-by-step explanation:
Mean (μ) = 220
σ= 16
n= 4
mean score(X) = 220 -12
= 208
Using central limit theorem which says that for a sample of size (n), the standard error is
standard deviation /√n
= 16/√4
= 16/2
= 8
Standard error = 8
Using Z score
Z = (μ - x) / standard error
Z= (220 -208)/8
Z= 12/8
Z= 1.5
From the table, Z = 1.5 = 0.4332
Since the normal distribution curve is symmetrical, we have
0.4332*2
= 0.8664
Percentage = 0.8664*100
= 86.64%
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