Question

8) What proportion of a normal distribution is located between each of the following z-score boundaries?

a. z = –0.25 and z = +0.25

b. z = –0.67 and z = +0.67

c. z = –1.20 and z = +1.20

13) A normal distribution has a mean of μ = 30 and a standard deviation of σ = 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body.

a. X = 33

b. X = 18

c. X = 24

d. X = 39

19) A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of μ = 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard deviation of σ = 2.5 hours and find the following values.

a. What is the probability of selecting an individual who uses electronic devices more than 12 hours a day?

b. What proportion of 8- to 18-year-old Americans spend between 5 and 10 hours per day using electronic devices? In symbols, p (5 < X < 10) = ?

Answer 1

Solution to question 8:

Answer to part a)

P(-0.25 < z < +0.25) = P(z < +0.25) - P(z < -0.25)

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Firat we find the P(z < -0.25) from the Z table

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P(z < -0.25) = 0.4013

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Now for P(z < 0.25) will be :

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P(z < 0.25) = 0.6368

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Thus we can see how these values get plotted on the normal curve , this will help us understand why we subtract the two values

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we need the area between -0.25 and +0.25 , the shaded region

Thus P(-0.25 < z < +0.25) = 0.6368 - 0.4013 = 0.2337

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Answer to part b)

P(-0.67 < z < +0.67) = P(z < +0.67) - P(z < -0.67)

P(z < +0.67) = 0.7486

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P(z < -0.67) = 0.2514

P(-0.67 < z < +0.67) = 0.7486 - 0.2514 = 0.4972

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Answer to part c)

P(-1.2 < z < +1.2) = P(z < 1.20 ) - P(z < -1.20)

P(z < 1.20) = 0.8849

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P( z < -1.20) = 0.1151

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P(-1.20 < z < +1.20) = 0.8849 - 0.1151 = 0.7698

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