Problem # 1 : IQs are known to be normally distributed with mean 100 and standar

Question

Problem # 1 : IQs are known to be normally distributed with mean 100 and standard deviation 15. (a) What percentage of people have an IQ lower than 86? (b) Fill in the blank. 75% of the population have an IQ that is greater than NOTE: Do not use the first half of the normal table (i.e., page 742 in the textbook, with negative z-values) because it will not be provided with the tests Enter your answer as a percentage, correct to 2 decimals, without the % sign. e.g., 28.31 Problem #1(a): 14.12 - Problem #1(b): 0.6786 answer correct to 2 decimals Just Save Submit Problem #1 for Grading Problem #1 | Attempt #1 | Attempt #2 | Attempt #3 Your Answer: 1(a) 14.121(a) 1(b) 0.6786 1(b) Your Mark: 1(a) 0/1x1(a) 1(b) 0/1x1(b) 1(a) 1(b) 1(a) 1(b)

Explanation / Answer

Solution:-
a) z(86) = (86-100)/15 = -14/15 = -0.9333

P(x < 86) = P(z > -0.9333) = 0.8238 = 82.38%

b) The z-value that has a greather than of 0.75 = 0.6744
x = z*sigma + mu
x = 0.6744*15+100
x = 110.116

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