Studies show that intelligence test scores or IQ follow a normal distribution (X) with a mean value of 100 and a standard deviation of 15. a. What is the probability that a randomly selected individual has an IQ higher than 90? Show your work by drawing a normal distribution that includes your answer. b. An IQ in the bottom 10% is considered to be low. What is the cutoff IQ for an individual to have a low IQ? Show your work by drawing a normal distribution that includes your answer. c. An IQ in the top 10% is considered to be high. What is the cutoff IQ for an individual to have a high IQ? Show your work by drawing a normal distribution that includes your answer.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Studies show that intelligence test scores or IQ follow a normal distribution (X) with a mean value of 100 and a standard deviation of 15.
a. What is the probability that a randomly selected individual has an IQ higher than 90? Show your work by drawing a normal distribution that includes your answer.
b. An IQ in the bottom 10% is considered to be low. What is the cutoff IQ for an individual to have a low IQ? Show your work by drawing a normal distribution that includes your answer.
c. An IQ in the top 10% is considered to be high. What is the cutoff IQ for an individual to have a high IQ? Show your work by drawing a normal distribution that includes your answer.
d. What are Q1, Q2, and Q3 of the distribution of X? Show your work by drawing a normal distribution that includes your answer.

 

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