Question #189616

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



1
Expert's answer
2021-05-07T13:08:52-0400

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<968610)P(Z<868610)=P(Z<1)P(Z<0)=0.84130.5=0.3413N=0.3413×5000=1706.5P(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<1068610)P(Z<968610)=P(Z<2)P(Z<1)=0.97720.8413=0.1359N=0.1359×5000=679.5P(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=0.56×5000=2800N = 0.56 \times 5000 = 2800


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