- A die was rolled several times, and the results are given in the following table. Construct a histogram for the data using the single-values 1, 2, 3, 4, 5, and 6.
| 5 | 3 | 1 | 1 | 4 | 2 | |
| 6 | 4 | 1 | 2 | 5 | 5 | |
| 4 | 3 | 1 | 6 | 4 | 2 | |
| 3 | 1 | 2 | 5 | 2 | 1 | |
| 4 | 6 | 5 | 1 | 4 | 5 | |
Do the data appear to be normally distributed? Explain. Choose one.
No, the histogram is left-tailed.
Yes, the histogram looks like a bell curve.
No, the histogram is relatively uniform.
Yes, the histogram is left-tailed.
Yes, the histogram is relatively uniform.
2. What percent of the standard normal z-distribution lies between the following values? (Round your answers to two decimal places.)
(a) z =
0 and z = 2
%
(b) z = −2 and z = 0
%
(c) z = −2 and z = 2 (Note: This
interval represents two standard deviations of the mean.)
%
3. Find the following probabilities. (Round your answers to four decimal places.)
(a) p(0 < z < 1.43)
(b) p(1.05 < z < 1.69)
(c) p(−0.89 < z < 1.75)
(d) p(z < −2.06)
(e) p(−2.35 < z < −1.17)
(f) p(z < 1.53)
4. Find c such that each of the following is true. (Round your answers to two decimal places.)
(a) p(0
< z < c) = 0.1308
c =
(b) p(c < z <
0) = 0.4849
c =
(c) p(−c < z < c)
= 0.4630
c =
(d) p(z > c)
= 0.6059
c =
(e) p(z > c)
= 0.0531
c =
(f) p(z < c)
= 0.1027
c =
5. The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard deviation of 0.4 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh the following amounts? (Round your answers to two decimal places.)
(a) less
than 14.6 ounces
%
(b) between 14.8 and 15.2 ounces
%
6. The amount of time between taking a pain reliever and getting relief is normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes. Find the probability that the time between taking the medication and getting relief is as follows. (Round your answers to four decimal places.)
(a) at
least 30 minutes
(b) at most 23 minutes
7. The shrinkage in length of a certain brand of blue jeans is normally distributed with a mean of 1.2 inches and a standard deviation of 0.4 inch. What percent of this brand of jeans will shrink the following amounts? (Round your answers to two decimal places.)
(a) more
than 1.7 inches
%
(b) between 1.1 and 1.35 inches
%
