Answer to Question #189616 in Statistics and Probability for CharQueen

Question

Given a population of 5000 score with the mean and . How many scores are:

Answer 1

Total problem:

given the population of 5000 scores with mean = 86 and standard deviation = 10.

How many score are:

a. between 86 and 96?

B. between 96 and 106?

c. Below 56%

a.

$P(86<X<96) = P(X<96) -P(X<86) \\ = P(Z< \frac{96-86}{10}) -P(Z< \frac{86-86}{10}) \\ = P(Z<1) -P(Z<0) \\ = 0.8413 - 0.5 \\ = 0.3413 \\ N = 0.3413 \times 5000 = 1706.5$

b.

$P(96<X<106) = P(X<106) -P(X<96) \\ = P(Z< \frac{106-86}{10}) -P(Z< \frac{96-86}{10}) \\ = P(Z<2) -P(Z<1) \\ = 0.9772-0.8413 \\ = 0.1359 \\ N = 0.1359 \times 5000 = 679.5$

c. $N = 0.56 \times 5000 = 2800$