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