Question

Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 16. Determine the percentage 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.

Answer 1

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%