Deck 9: The Normal Distribution

Question 1

Which of the following distributions is not continuous?

A) normal distribution
B) uniform distribution
C) exponential distribution
D) binomial distribution

Answer 1

binomial distribution

Question 2

Which of the following is always true for a normal distribution?

A) $P(x>8)=P(x \geq 9)$
B) $P(2x \leq 8)=P(2 \leq x<8)$
C) $P(x<5) \neq P(x \leq 5)$
D) $P(x \leq 8)=P(x \leq 8.5)$

Answer 2

$P(2x \leq 8)=P(2 \leq x<8)$

Question 3

If we are using the normal approximation to determine the probability of at most 28 successes in a binomial distribution $(P(x \leq 28))$ , the normal distribution probability that is used to make the estimate is

A) $P(x \leq 27.5)$ .
B) $P(x \leq 28)$ .
C) $P(x \leq 28.5)$ .
D) $P(x<28)$ .

Answer 3

$P(x \leq 28.5)$ .

Question 4

When considering area under the standard normal curve, decide whether the area to the right of $z=2$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

A) bigger than
B) smaller than
C) equal to

Question 5

When considering area under the standard normal curve, decide whether the area to the left of $z=-2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

A) equal to
B) bigger than
C) smaller than

Question 6

When considering area under the standard normal curve, decide whether the area to the left of $z=-2.5$ is bigger than, smaller than, or equal to the area to the right of $z=2$ .

A) smaller than
B) bigger than
C) equal to

Question 7

When considering area under the standard normal curve, decide whether the area to the left of $z=0$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=-0.2$ .

A) smaller than
B) bigger than
C) equal to

Question 8

When considering area under the standard normal curve, decide whether the area to the left of $z=2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

A) bigger than
B) smaller than
C) equal to

Question 9

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=-1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=2$ and $\mathrm{z}=2.5$ .

A) bigger than
B) smaller than
C) equal to

Question 10

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=1.1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=-1.1$ and $\mathrm{z}=1.5$ .

A) equal to
B) bigger than
C) smaller than

Question 11

When considering area under the standard normal curve, decide whether the area between $z=-0.2$ and $z=0.2$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=-0.3$ and $\mathrm{z}=0.3$ .

A) smaller than
B) bigger than
C) equal to

Question 12

For the uniform distribution pictured below, the probability $P(2 \leq x \leq 2.5)$ equals

A) $1 / 6$ .
B) 1 .
C) 1.3 .
D) none of these

Question 13

For the uniform distribution pictured below, the probability $P(x=2)$ equals

A) 0 .
B) $1 / 3$ .
C) $2 / 3$ .
D) none of these

Question 14

For the uniform distribution pictured below, the probability $P(x \leq 2.5)$ equals

A) $5 / 6$ .
B) 1 .
C) $1 / 3$ .
D) none of these

Question 15

The area to the right of $z=1.0$ is equal to

A) 0.3413 .
B) 0.8413 .
C) 0.6816 .
D) 0.1587 .

Question 16

To determine the probability of obtaining exactly 20 successes in 50 trials with $p=0.30$ , we should use

A) the binomial formula.
B) the Poisson formula.
C) the normal approximation to the binomial distribution.
D) the normal table.

Question 17

The probability of obtaining exactly 20 successes in 50 trials

A) is equal to 0 .
B) can be approximated by using the normal table with $x$ between 19.5 and 20.5.
C) can only be approximated by the binomial formula.
D) cannot be found using the normal table.

Question 18

The problem that is solved by using the standard formula table and the formula $\mu=n p$

A) involves Table V.
B) involves the normal approximation to the binomial distribution.
C) originally involved the normal approximation.
D) originally involved the Poisson distribution.

Question 19

In a binomial distribution with 10 trials, which of the following is true?

A)
B) $P(x<4)=P(x \geq 5)-P(x \geq 4)$
C) $P(x<6)=1-P(x \geq 7)$
D) $P(x>7)=P(x \geq 8)$

Question 20

If $x$ is a normal random variable with $\mu=50$ and $\sigma=6$ , then the probability that $x$ is not between 44 and 56 is

A) 0.6826 .
B) 0.3413 .
C) 0.8413 .
D) 0.3174 .

Question 21

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated.

-Between -1 and 1

Question 22

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated.

-Between $1 / 2$ and $3 / 2$

Question 23

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated.

-Between -2 and -1

Question 24

Find the standard normal-curve area indicated using the normal table.
-Between $\mathrm{z}=-1.3$ and $\mathrm{z}=-0.4$

Question 25

Find the standard normal-curve area indicated using the normal table.
-To the left of $z=0.67$

Question 26

Find the standard normal-curve area indicated using the normal table.
-To the left of $z=-0.54$

Question 27

If a random variable has the normal distribution with $\mu=30$ and $\sigma=5$ , find the probability that it will take on the indicated value.
-Less than 32

Question 28

If a random variable has the normal distribution with $\mu=30$ and $\sigma=5$ , find the probability that it will take on the indicated value.
-Between 31 and 35

Question 29

If a random variable has the normal distribution with $\mu=30$ and $\sigma=5$ , find the probability that it will take on the indicated value.
-Between 24 and 28

Question 30

Find the following $z$ values.

-z_0.05

Question 31

Find the following $z$ values.

-z_0.45

Question 32

Find the following $z$ values.

-z_0.65

Question 33

Find the following $z$ values.

-z_0.90

Question 34

Find $z$ if the normal curve area to the right of $z$ is 0.8997 .

Question 35

Find $z$ if the normal curve area to the left of $z$ is 0.1611 .

Question 36

A normal distribution has mean $\mu=60$ . If $15.87 \%$ of the area under the curve is to the left of 54 , find the area to the right of 64.

Question 37

A normal distribution has mean $\mu=60$ . If $15.87 \%$ of the area under the curve is to the left of 54 , find the area between 58 and 63 .

Question 38

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces.
-Find the probability that more than 16 ounces is dispensed in a cup.

Question 39

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces.
-Find the probability that between 15 and 18 ounces are dispensed in a cup.

Question 40

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces.
-Find the number of ounces above which $80 \%$ of the dispensed sodas will fall. Round to the nearest tenth.

Question 41

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time
-at least 60 products will be successful.

Question 42

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time
-at most 50 products will be successful.

Question 43

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time
-between 55 and 59 products, inclusive, will be successful.

Question 44

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes.
-Find the probability that a customer spends less than 48 minutes in the supermarket.

Question 45

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes.
-Find the probability that a customer spends between 39 and 43 minutes in the supermarket.

Question 46

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes.

-Find the number of minutes, $m$ , for which the probability that a customer spends less than minutes in the supermarket is 0.10 . Round your answer to the nearest tenth.

Question 47

It has been estimated that $40 \%$ of the televisions that a manufacturer makes need repairs in the first three years of operation. A new hotel buys 90 televisions from this company. Find the probability that in the first three years of operation
-less than 32 of the televisions need repairs.

Question 48

It has been estimated that $40 \%$ of the televisions that a manufacturer makes need repairs in the first three years of operation. A new hotel buys 90 televisions from this company. Find the probability that in the first three years of operation
-between 38 and 42 of the televisions, inclusive, need repairs.

Question 49

The waiting time in a doctor's office has an exponential distribution with $\mu=45$ minutes. Find the probability that
-a patient has to wait between 0 and 30 minutes.

Question 50

The waiting time in a doctor's office has an exponential distribution with $\mu=45$ minutes. Find the probability that
-a patient has to wait between 35 and 50 minutes.

Question 51

Find the indicated normal-curve area using the normal table.
-Between $z=-1.48$ and $z=0$

Question 52

Find the indicated normal-curve area using the normal table.
-Between $\mathrm{z}=-1.23$ and $\mathrm{z}=0.56$

Question 53

Find the indicated normal-curve area using the normal table.
-Between $\mathrm{z}=-1.23$ and $\mathrm{z}=1.23$

Question 54

Find the indicated normal-curve area using the normal table.
-Between $\mathrm{z}=1.23$ and $\mathrm{z}=2.34$

Question 55

Find the indicated normal-curve area using the normal table.
-To the left of $z=-1.5$ .

Question 56

Find the indicated normal-curve area using the normal table.
-Between $z=-1.3$ and $z=1$ .

Question 57

Find the indicated normal-curve area using the normal table.
-Between $z=-2$ and $z=-1$ .

Question 58

Find $z$ if the normal curve area to the left of $z$ is 0.3015.

Question 59

Find $z$ if the normal curve area between 0 and $z$ is 0.4345 .

Question 60

Find $z$ if the normal curve area between $-z$ and $z$ is 0.9512 .

Question 61

Find $z$ if the normal curve area to the left of $z$ is 0.8962 .

Question 62

Find $z$ if the normal curve area to the right of $z$ is 0.3483 .

Question 63

Find $z$ if the normal curve area to the right of $z$ is 0.8665 .

Question 64

A salesperson knows that $20 \%$ of her presentations result in sales. Find the probabilities that in the next 60 presentations}
-at least 9 result in sales.

Question 65

A salesperson knows that $20 \%$ of her presentations result in sales. Find the probabilities that in the next 60 presentations}
-between 14 and 18, inclusive, result in sales.

Question 66

A machine pours beer into $16 \mathrm{oz}$ . bottles. Experience has shown that the number of ounces poured is normally distributed with a standard deviation of 1.5 ounces. Find the probabilities that the amount of beer the machine will pour into the next bottle will be
-more than 17 ounces.

Question 67

A machine pours beer into $16 \mathrm{oz}$ . bottles. Experience has shown that the number of ounces poured is normally distributed with a standard deviation of 1.5 ounces. Find the probabilities that the amount of beer the machine will pour into the next bottle will be
-between 12 and 14 ounces.

Question 68

The annual number of earthquakes in a certain region is a random variable having approximately a normal distribution with $\mu=15.7$ . What is the standard deviation of this distribution if the probability is 0.70 that there will be at least 14 earthquakes? Round answer to the nearest tenth.

Question 69

The probability is 0.26 that a cloud seeded with silver iodide will fail to show spectacular growth. Use the normal approximation to the binomial distribution to find the probability that among 50 clouds seeded with silver iodide only 13 will fail to show spectacular growth. Round answer to the nearest hundredth.

Question 70

The equation $f(x)=0.125$ can serve as the probability density function of a random variable that takes on values on the interval from 1 to 8 .

Question 71

The equation $f(x)=\frac{1}{6}(2 x-3)$ can serve as a probability density of a random variable that takes on values on the interval from 1 to 3.

Question 72

The continuity correction is always used in the problems involving the normal distribution.

Question 73

The normal approximation to the binomial distribution applies in problems that originally involve the normal distribution.

Question 74

The $z$ value such that the area to the left of $z$ is 0.05 is located to the left of zero on the $z$ -axis.

Question 75

then $x$ must be a discrete random variable.

Question 76

If the area in the standard normal distribution is on the left side of zero, then that area has a negative value.

Question 77

It is never desirable to use the normal approximation to the binomial distribution to solve binomial problems that can be solved by using Table V.

Question 78

The formula $\mu=n p$ is used to convert any normally distributed variable to one which has a mean of 0 and a standard deviation of 1.

Question 79

The formula $\sigma=\sqrt{n p(1-p)}$ finds the standard deviation in problems which originally involve the binomial distribution.

Question 80

The mean of every normal distribution is equal to 0.