Chapter 6: Continuous Probability Distributions

1.  A continuous uniform random variable x has a lower bound of a = -3, an upper bound of b = 5. What is p(x > -1)?

1. 0.2500
2. 0.5000
3. 0.1250
4. 0.7500 X

Solution:

> 1 - punif(-1, min = -3, max = 5)

[1] 0.75

or

> punif(-1, min = -3, max = 5, lower.tail = FALSE)

[1] 0.75

2.  A continuous uniform random variable x has a lower bound of a = -21, an upper bound of b = -6.  What value of x provides an area in the upper tail equal to 0.20?

1. -18
2. -15
3. -12
4. -9 X

Solution:

> qunif(0.80, min = -21, max = -6)

[1] -9

or

> qunif(0.20, min = -21, max = -6, lower.tail = FALSE)

[1] -9

3.  If z is the standard normal random variable, what is p(z < 0.275)?

1. 0.5683
2. 0.6083 X
3. 0.6983
4. 0.7983

Solution:

> pnorm(0.275)

[1] 0.6083419

4.  If z is the standard normal random variable, what is p(-1.5 < z < 1.125)?

1. 0.7329
2. 0.6929
3. 0.8029 X
4. 0.8329

Solution:

> pnorm(1.125) - pnorm(-1.5)

[1] 0.8028983

5.  If z is the standard normal random variable, what is p(z > -1.787)?

1. 0.8530
2. 0.9630 X
3. 0.7730
4. 0.8230

Solution:

> 1 - pnorm(-1.787)

[1] 0.9630313

or

> pnorm(-1.787, lower.tail = FALSE)

[1] 0.9630313

6.  If z is the standard normal random variable, what value of z provides an area in the upper tail of 0.25?

1. 0.6745 X
2. 0.6245
3. 0.7745
4. 0.6945

Solution:

> qnorm(0.75)

[1] 0.6744898

or

> qnorm(0.25, lower.tail = FALSE)

[1] 0.6744898

7.  If x is a normally-distributed random variable with a mean of 100 and a standard deviation of 15, what is p(x  < 115)?

1. 0.8813
2. 0.9113
3. 0.7713
4. 0.8413 X

Solution:

> pnorm(115, 100, 15)

[1] 0.8413447

8.  If x is a normally-distributed random variable with a mean of 78 and a standard deviation of 12, what is p(67 < x < 81)?

1. 0.3890
2. 0.4190 X
3. 0.4590
4. 0.4790

Solution:

> pnorm(81, 78, 12) - pnorm(67, 78, 12)

[1] 0.4190477

9.  If x is a normally-distributed random variable with a mean of -84 and a standard deviation of 10, what is p(-94 < x < -74)?

1. 0.6827 X
2. 0.7227
3. 0.6527
4. 0.6227

Solution:

> pnorm(-74, -84, 10) - pnorm(-94, -84, 10)

[1] 0.6826895

10.   If x is a normally-distributed random variable with a mean of -5 and a standard deviation of 15, what value of x provides an area of 0.025 in the lower tail?

1. -31.39946
2. -38.39946
3. -34.39946 X
4. -44.39946

Solution:

> qnorm(0.025, -5, 15)

[1] -34.39946