A variable is normally distributed with mean 66 and standard deviation 22. a. De

ID: 3364660 • Letter: A

Question

A variable is normally distributed with mean

and standard deviation

22.

a. Determine the quartiles of the variable.

b. Obtain and interpret the

9090th

percentile.

c. Find the value that 65% of all possible values of the variable exceed.

Bold d. nbspd.

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.

Bold d. nbspd.

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.

a) The quartiles can be obtained by finding the 50% Confidence interval.

For 0.5 significance level, zcrit = 0.67

1st quartile = Mean - Zcrit * SD = 66 - 0.67*22 = 51.26

2nd quartile = Mean = 66

3rd quartile = Mean + Zcrit * SD = 66 + 0.67*22 = 80.74

b) P(X < x) = 0.9
Z = -1.28
-1.28 = (x - mean)/sd
x = -1.28*22 + 66 = 37.84

90% of the data lies below x = 37.84

d) 95% Confidence interval
Zcrit = 1.96

95% CI = Mean +/- Zcrit * SD
95% CI = 66 +/- 1.96*22 = (22.88, 109.12)

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.