A variable is normally distributed with mean 9 and standard deviation 3. a. Dete

Question

A variable is normally distributed with mean 9 and standard deviation 3. a. Determine the quartiles of the variable. b. Obtain and interpret the 90th percentile. C. Find the value that 65% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025. Interpret the answer. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. . (Round to two decimal places as needed.)

Explanation / Answer

Data given:

Mean, m = 9

Standard Deviation, S = 3

(a)

For the first quartile (25%), the corresponding z-score is:

z = -0.67

So,

(X-m)/S = -0.67

Putting values:

(X-9)/3 = -0.67

Solving we get:

X = 6.99

For the third quartile (75%), the corresponding z-score is:

z = 0.67

So,

(X-m)/S = 0.67

Putting values:

(X-9)/3 = 0.67

Solving we get:

X = 11.01

So we have:

Q1 = 6.99, Q2 = 9, Q3 = 11.01

(b)

For the 25% percentile, the corresponding z-score is:

z = 1.28

So,

(X-m)/S = 1.28

Putting values:

(X-9)/3 = 1.28

Solving we get:

X = 12.84

So 90% of all the values lie below the score of 12.84

Hope this helps !

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