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A set of 7,500 scores on a test are distributed normally, with a mean of 23 and a standard deviation of 4. To the nearest integer value, how many scores are there between 21 and 25?

User Jagguli
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2 Answers

2 votes

Answer:

Explanation:

User Hein Zaw Htet
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1 vote

Answer: The number of scores between 21 and 25 is 2872

Explanation:

Since the test scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = test scores

u = mean test score

s = standard deviation

From the information given,

u = 23

s = 4

We want to find the probability test scores between 21 points and 25. It is expressed as

P(21 lesser than or equal to x lesser than or equal to 25)

For x = 21,

z = (21 - 23)/4 = - 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.30854

For x = 25,

z = (25 - 23)/4 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69146

P(21 lesser than or equal to x lesser than or equal to 25)

= 0.69146 - 0.30854 = 0.38292

The number of scores between 21 and 25 would be

0.38292 × 7500 = 2872

User Josh Holloway
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