# Statistics with R

## Student Resources

# 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)?

- 0.2500
- 0.5000
- 0.1250
- 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?

- -18
- -15
- -12
- -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)?

- 0.5683
- 0.6083 X
- 0.6983
- 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)?

- 0.7329
- 0.6929
- 0.8029 X
- 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)?

- 0.8530
- 0.9630 X
- 0.7730
- 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?

- 0.6745 X
- 0.6245
- 0.7745
- 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)?

- 0.8813
- 0.9113
- 0.7713
- 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)?

- 0.3890
- 0.4190 X
- 0.4590
- 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)?

- 0.6827 X
- 0.7227
- 0.6527
- 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?

- -31.39946
- -38.39946
- -34.39946 X
- -44.39946

**Solution:**

> qnorm(0.025, -5, 15)

[1] -34.39946