QUESTION 9 Choose the one alternative that best completes the statement or answe

Question

QUESTION 9 Choose the one alternative that best completes the statement or answers the question Solve the problem. Scores on a test have a mean of 70 and Q3 is 83. The scores have a distribution that is approximately normal. Find Pgo. (You will need to first find the standard deviation.) O A 956 O B.948 O C. 92.9 O D. 93.7 QUESTION 10 A bank's loan officer rates applicants for credit The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220 O A 0 2257 B. 0 0703 C.0.3811 D.0.1554

Explanation / Answer

1. Q3 means 3rd quartile or 75%ile. thus for 0.75, the z value from the normal distribution table is 0.68

thus Q3=Mean+z*s

here it is 83=70+0.68*s

or s is 19.11765

for P90 or 90%ile, the z value form normal distribution table is 1.28

thus answer is mean+z*s =70+1.28*19.11765 =94.8 or option B

2. mean is 200 and s is 50

the z value is given as (x-mean)/s

P(170<x<220)=P((170-200)/50<z<(220-200)/50)=P(-0.6<z<0.4) or P(z<0.4)-P(z<-0.6)=P(z<0.4)-(1-P(z<0.6))

from normal distribution table we get 0.6554-(1-0.7257)=0.3811 option C

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