Deck 6: Continuous Random Variables

Question 1

In a statistical study,the random variable X = 1 if the house is colonial,and X = 0 if the house is not colonial.The random variable X is continuous.

Answer 1

False

Question 2

The z value tells us the number of standard deviations that a value x is from the mean.

Answer 2

True

Question 3

The mean of a standard normal distribution is always equal to 1.

Answer 3

False

Question 4

The standard deviation of a standard normal distribution is always equal to 1.

Question 5

The mean and median are the same for a normal distribution.

Question 6

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

Question 7

For a continuous distribution,the exact probability of a particular value is zero.

Question 8

A continuous random variable may assume only integer values in a given interval.

Question 9

If the distances between the ordered data values are proportional to the distances between the actual values,then the normal probability plot will be a straight line.

Question 10

For a binomial probability experiment,with n = 150 and p = .2,it is appropriate to use the normal approximation to the binomial distribution.

Question 11

All continuous random variables are normally distributed.

Question 12

The normal probability distribution is a discrete probability distribution.

Question 13

A uniform distribution f(x)is a continuous probability distribution,which says the probability that x is in any 2 intervals of equal length is the same.

Question 14

The actual weight of hamburger patties is an example of a continuous random variable.

Question 15

For a continuous distribution,P(X £ 100)= P(X < 100).

Question 16

The mean and median are the same for an exponential distribution.

Question 17

The exponential probability distribution is based on a continuous random variable.

Question 18

If the random variable x is normally distributed,68.26 percent of all possible observed values of x will be within two standard deviations of the mean.

Question 19

For a continuous random variable x,the height of the probability curve f(x)at a particular point indicates the value of the probability for that value.

Question 20

A continuous probability distribution having a rectangular shape,where the probability is evenly distributed over an interval of numbers,is called a uniform probability distribution.

Question 21

The mean life of a pair of shoes is 40 months with a standard deviation of 8 months.If the life of the shoes is normally distributed,how many pairs of shoes out of one million will need replacement before 36 months?

A) 500,000
B) 808,500
C) 191,500
D) 308,500

Question 22

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

A) normal
B) exponential
C) Poisson
D) binomial
E) uniform

Question 23

If the random variable X has a mean of µ and a standard deviation σ,then the mean and standard deviation,respectively,of (X − µ)/σ are

A) μ and σ.
B)
And s.
C) 1 and 0.
D) 0 and 1.

Question 24

Values of the standard normal random variable are measured

A) with reference to specific units.
B) in the units in which the mean is measured.
C) in the number of standard deviations from the mean.
D) in squared units in which the mean is measured.
E) None of the choices is correct.

Question 25

It is appropriate to use the uniform distribution to describe a continuous random variable x when

A) the area under the probability curve = 1.
B) the probability curve f(x)> 0.
C) the shape of the histogram of all possible values of x is nonsymmetrical.
D) relative frequencies of all possible values of x are about the same.

Question 26

In order to approximate the binomial distribution using the normal distribution,the following condition(s)must be met if p is near 1.

A) np > 5 only
B) n must be larger than just meeting the condition of np > 5.
C) n can be as small as np > 5.
D) n > 5

Question 27

Which of the following is a continuous distribution?

A) Poisson
B) hypergeometric
C) exponential
D) binomial

Question 28

A standard normal distribution has a mean of ____________ and standard deviation of ____________.

A) zero,zero
B) zero,one
C) one,one
D) one,zero

Question 29

The ___________ is a graphic that is used to check visually whether data come from a normal population.

A) exponential plot
B) normal probability plot
C) box-and-whiskers plot
D) normal distribution graph

Question 30

The relationship between the standard normal random variable z and normal random variable X is that

A) only the normal random variable X is continuous.
B) only the standard normal variable z is continuous.
C) the standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
D) the values of the standard normal random variable z cannot be negative.
E) the values of the normal random variable X cannot be negative.

Question 31

If the wages of workers for a given company are normally distributed with a mean of $15 per hour,then the proportion of the workers earning more than $13 per hour

A) is greater than the proportion earning less than $13 per hour.
B) is greater than the proportion earning less than $18 per hour.
C) is less than 50 percent.
D) is less than the proportion earning more than the mean wage.

Question 32

A property of continuous distributions is that

A) as with discrete random variables,the probability distribution can be approximated by a smooth curve.
B) probabilities for continuous variables can be approximated using discrete random variables.
C) unlike discrete random variables,probabilities can be found using tables.
D) unlike discrete random variables,the probability that a continuous random variable equals a specific value is zero [P(X = x)= 0].

Question 33

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

A) less than
B) greater than
C) equal to
D) less than,greater than,or equal to,depending on the value of the mean,
E) less than,greater than,or equal to,depending on the value of the standard deviation,

Question 34

The grade a student received on an examination was transformed to a z value,which was negative.Therefore,we know that he scored

A) higher than 16 percent of the class.
B) higher than 45 percent of the class.
C) above the first quartile.
D) below the mean.
E) lower than 16 percent of the class.

Question 35

The standardized normal quantile value O_i is the z value that gives an area of i/(n − 1)to its right under the normal curve.

Question 36

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution.In this industry,a firm with a standard normal variable value of z = 1

A) has an above average price-to-earnings ratio.
B) has a below average price-to-earnings ratio.
C) has an average price-to-earnings ratio.
D) may have an above average or below average price-to-earnings ratio.

Question 37

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams.We calculated the value of z for a specific box of this brand of cereal,and the z value was negative.This negative z value indicates that

A) we made a mistake in our calculations,as z must always be a nonnegative number.
B) the fill weight exceeds 910 grams.
C) the fill weight is less than 910 grams.
D) the fill weight is equal to 910 grams.
E) the fill weight may be more or less than 910 grams depending on the value of the standard deviation.

Question 38

The normal approximation of the binomial distribution is appropriate when

A) np ≥ 5.
B) n(1 − p)≥ 5.
C) np ≤ 5.
D) n(1 − p)≤ 5 and np ≤ 5.
E) np ≥ 5 and n(1 − p)≥ 5.

Question 39

The first step to constructing a normal probability plot is to

A) calculate O_i.
B) compute area i/(n + 1).
C) construct a box-and-whiskers plot.
D) order the values in the data.

Question 40

The random variable x has a uniform distribution when x lies between the values of 4 and 10.When x = 10,what is the value of f(x)?

A) 0
B) 1
C) 1/6
D) 1/14