Question 1 What is the area under the normal distribution cu

Question 1

What is the area under the normal distribution curve to the left of z = 0.87?

0.3078

0.8078

0.1922

0.6922

1 points

Question 2

What is the z-value to the right of the mean where 59.18% of the distribution lies to the left of it?

z = 0.23

z = 1.33

z = -0.23

z = 0.24

1 points

Question 3

What z-value corresponds to the 18th percentile?

z = -0.47

z = 0.47

z = -0.13

z = -0.92

1 points

Question 4

Using the standard normal distribution, what is P(-2.32 < z < 1)?

0.1485

0.8515

0.6811

0.8311

1 points

Question 5

At a large department store, the average number of years of service was 13.5 with a standard deviation of 6.2 years. If an employee is picked at random, what is the probability that the employee has worked for the company between 8 and 20 years?

0.6641

0.6125

0.6664

0.6637

1 points

Question 6

Using the standard normal distribution, what is P(z > 2.09)?

0.4817

0.0183

0.0019

0.5183

1 points

Question 7

What is the z-value to the right of the mean where 8.05% of the distribution lies to the right of it?

z = -1.40

z = 1.40

z = 0.20

z = 0.51

1 points

Question 8

The average hourly wage of workers at a fast food restaurant is $5.85 with a standard deviation of $0.35. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability the worker earns more than $6.50 an hour?

0.4686

0.0314

0.0322

0.9686

1 points

Question 9

Using the standard normal distribution, what is P(1.8 < z < 2.39)?

0.0275

0.2224

0.0443

0.9557

1 points

Question 10

In a given normal distribution, if the mean is 500 and 3.62% of the distribution lies to the right of 572, what is the standard deviation?

80

40

130

50

1 points

Question 11

What is the area under the normal distribution curve to the right of z = 0.58?

0.2190

0.7190

0.2810

0.7810

1 points

Question 12

What is the area under the normal distribution curve between z = -1.89 and z = 0?

0.4706

0.9706

0.0294

0.5294

1 points

Question 13

What z-value corresponds to the 63rd percentile?

z = 1.13

z = -0.33

z = 0.33

z = 0.24

1 points

Question 14

In a given normal distribution, the standard deviation is 14.4 and 8.27% of the distribution lies to the left of 60. What is the mean?

80

40

63

72

1 points

Question 15

At Northwest Nursing School, the average score a student must make on an entrance exam is 142 points with a standard deviation of 16 points. If the nursing school can only accept the top 15% of the applicants, what is the cutoff score a nurse must make to be considered for this school?

148 or above

159 or above

157 or above

149 or above

1 points

Question 16

Using the standard normal distribution, what is P(z < -0.35)?

0.1368

0.6368

0.3632

0.3594

1 points

Question 17

What is the area under the normal distribution curve between z = -2.01 and z = -1.89?

0.0072

0.9484

0.0478

0.0516

1 points

Question 18

The average weight of a box of cereal is 25.2 ounces with a standard deviation of 0.18 ounces. Quality control wants to make certain that the 10% heaviest boxes of cereal are not sent to stores to sell. What would be the cutoff weight for these cereal boxes?

25.43 ounces or above

24.97 ounces or above

25.25 ounces or above

25.36 ounces or above

1 points

Question 19

A new hockey franchise is planning to begin league play in the 2004 season. They want to price their tickets in the middle 64% range. If the average price of a ticket is $20 with a standard deviation of $3.50, what are the minimum and maximum prices that this franchise should charge?

$16.50 to $23.50

$16.81 to $23.19

$16.78 to $23.22

$18.74 to $21.26

1 points

Question 20

The lengths of bolts produced at a factory are normally distributed with a mean of .75 inches and a standard deviation of .03 inches. What is the probability that a randomly selected bolt has a length of less than .82 inches?

0.9901

0.0099

0.4901

0.5000

		0.3078
		0.8078
		0.1922
		0.6922

Solution

(1) P(z < 0.87) =0.8078 (from standard normal table)

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(2)P(Z>z)=0.5918

--> z=0.23 (from standard normal table)

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(3)z = -0.92(from standard normal table)

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(4)P(-2.32 < z < 1) = 0.8311(from standard normal table)

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(5)P(8<X<20) = P((8-13.5)/6.2 <Z<(20-13.5)/6.2)

=P(-0.89<Z<1.05) =0.6664(from standard normal table)

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(6)P(z > 2.09) =0.0183(from standard normal table)

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(7)z = -1.40

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(8)P(X>6.5) = P(Z>(6.5-5.85)/0.35)

=P(Z>1.86) =0.0314

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(9) P(1.8 < z < 2.39) =0.0275

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(10)

P(X<x)=1-0.0362

--> P(Z<(572-500)/s) =0.9638

--> (572-500)/s = 1.797

So s= (572-500)/ 1.797 =40

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(11)0.2810

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(12)0.4706

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(13)z = 0.33

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(14)P(Z<(60-mean)/14.4) =0.0827

--> (60-mean)/14.4 = -1.39 (from standard normal table)

So mean = 60+1.39*14.4 =80.016

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(15)

P(X<c)=0.85

--> P(Z<(c-142)/16)=0.85

--> (c-142)/16 =1.04 (from standard normal table)

So c= 142+1.04*16=158.64

Answer: 159 or above

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(16)0.3632

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(17)0.0072

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(18)

P(X<c) = 0.9

--> P(Z<(c-25.2)/0.18)=0.9

--> (c-25.2)/0.18 = 1.28 (from standard normal table)

So c=25.2+1.28*0.18 =25.4304

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(19)$16.78 to $23.22

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(20)P(X<0.82) = P(Z<(0.82-0.75)/0.03)

=P(Z<2.33) =0.9901