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Take a Test - Mohannad almalki Secure | https://wwww.mathd.com/Student/PlayerTest.aspx?testid-174881912&centerwinayes; MTH2502-02 STATISTICS SPRING 2018 Mohannad almalk Quiz: Quiz CH6 Time Remaini This Question: 1 pt 6017(0 complete) Assume that adults have IQ scores that are normally distributed with a mean of -100 and a standard deviation 15. a. Find the percentage of adults that have an IQ between 84 and 116. b. Find the percentage of adults that have an IQ exceeding 119. c. Determine the quartiles for adult IQs d. Obtain the 95th percentile for the IQ of adults. a.The percentage of adults that have an IQ between 84 and 116is 1%. Type an integer or decimal rounded to two decimal places as needed.) b.The percentage of adults that have an IQ exceeding 119D%. Type an integer or decimal rounded to two decimal places as needed.) c. The first quartile is Type an integer or decimal rounded to two decimal places as needed.) The second quartile is Type an integer or decimal rounded to two decimal places as needed.) The third quartile is Type an integer or decimal rounded to two decimal places as needed.) d. The 95th percentile is Enter your answer in each of the answer boxes. MacBook Ai

Explanation / Answer

We have been given params of normal distribution, to be used for normalizing the distribution:

Mean = 100

Stdev = 15

a. P(84<X<116) = P(84-100/15<Z< 116-100/15) = P(-1.067<Z<1.067) = .8569-.1431 = .7138 or 71.38%

b. P(X>119) = P(Z> 119-100/15) = .8974 or 89.74%

c. 1st quartile is quartile for adult IQs with 25% as cutoff= P(X<c) = .25

P(Z< c-100 / 15) = .25,
So, Z = -.675 from the Z tables

(c-100)/15 = -.675
c = 15*-.675+100 = 89.975
So, 89.975 or 90.00 ( rounded off to 2 digit) is the 1st quartile

2nd quartile is median basically and is equal to the mean. = 100

3rd quartile is cutoff for 75th percentile -
P(Z< c-100 / 15) = .75,
So, Z = +.675 from the Z tables

(c-100)/15 = .675
c = 15*.675+100 = 110.125
So, 110.13 ( rounded off to 2 digit) is the 3rd quartile

d. P(X<c) = .95
So, c = 1.645*15+100 = 125.68

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