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Chapter 6: Q. 23 (page 356)

23. ITBS scores The Normal distribution with mean μ=6.8and standard deviation σ=1.6is a good description of the Iowa Test of Basic Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of a randomly chosen student Xfor short. Find P(X≥9)and interpret the result. Follow the four-step process.

Short Answer

Expert verified

The probability for P(X≥9)is 0.0838. There is 8.38%chances that student's score is 9or more.

Step by step solution

01

Given information

The Normal distribution with mean μ=6.8and a standard deviation of σ=1.6.

02

Explanation

Let Xbe a random variable with a mean of 6.8and a standard deviation of 1.6and a normal distribution.

Thez-score is calculated by dividing the value reduced by the mean by the standard deviation:
z=x-μσ
Where, xindicates raw score, μindicates population mean, andσ indicates the population standard deviation.
P(X≥9)can be calculated as:

P(x≥9)=Px−μσ≥9−μσ=Pz≥9−6.81.6=P(Z≥1.38)=0.0838

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Most popular questions from this chapter

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(a) It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain \(1250in premiums. But if he were to die, you would lose almost \)100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.

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