- The weights (in
grams) of several bags of chocolate chip cookies are given in the following
table. Construct a histogram for the data using the groups 420 ≤ x <
430, 430 ≤ x < 440, . . . , 480 ≤ x < 490.
| 451 | 435 | 482 | 449 | 454 | 451 |
| 479 | 448 | 432 | 423 | 461 | 475 |
| 467 | 453 | 448 | 459 | 454 | 444 |
| 475 | 461 | 450 | 466 | 446 | 458 |
| |
Do the data
appear to be approximately normally distributed? Explain.
1.Yes, the histogram is relatively uniform.
2.No, the histogram is left tailed.
3.No, the data looks random.
4.Yes, the histogram looks like a bell curve.
5.No, the histogram is right tailed.
- 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 = 1
___ %
(b) z = −1 and z = 0
___ %
(c) z = −1 and z = 1 (Note: This interval represents one standard deviation of the mean.)
___ %
- 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 = 1.5
___%
(b) z = −1.5 and z = 0
___%
(c) z = −1.5 and z = 1.5 (Note: This interval represents one and one-half standard deviations of the mean.)
___%
- A population is
normally distributed with mean 18.9 and
standard deviation 1.3.
(a) Find the intervals representing one, two, and
three standard deviations of the mean.
one standard deviation _____ (smaller value)
_____ (larger value)
two standard deviations _____ (smaller value)
_____ (larger value)
three standard deviations _____ (smaller value)
_____ (larger value)
(b)
What percent of the data lies in each of the intervals in part (a)? (Round your
answers to two decimal places.)
| one standard deviation | % |
| two standard deviations | % |
| three standard deviations | % |
(c) Choose a
sketch of the bell curve.
| |
5. Find the following probabilities. (Round your answers to four decimal places.)
(a) p(0 < z < 1.62)
(b) p(1.40
< z < 1.84)
(c) p(−0.37 < z < 1.55)
(d) p(z < −1.93)
(e) p(−1.33 < z < −0.87)
(f) p(z < 1.27)
6.The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard deviation of 0.2 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 14.5 ounces
___ %
(b) between 14.7 and 15.3
ounces
___ %
7.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 3 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 34 minutes
______
(b) at most 21 minutes
______
