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An unknown distribution has a mean of $80$and a standard deviation of $12$. A sample size of $95$is drawn randomly from the population.

Find the probability that the sum of the $95$values is greater than $7650$.

70. Which of the following is NOT TRUE about the distribution for averages?

a. The mean, median, and mode are equal.

b. The area under the curve is one.

c. The curve never touches the x-axis.

d. The curve is skewed to the right.

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $\backslash (4.59$and a standard deviation of $\backslash )0.10$. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the $16$gas stations. The distribution to use for the average cost of gasoline for the $16$gas stations is:

a.$\stackrel{¯}{X}~N(4.59,0.10)$

b.$\stackrel{¯}{X}~N\left(4.59,\frac{0.10}{\sqrt{16}}\right)$

c.$\stackrel{¯}{X}~N\left(4.59,\frac{16}{0.10}\right)$

d.$\stackrel{¯}{X}~N\left(4.59,\frac{\sqrt{16}}{0.10}\right)$

An unknown distribution has a mean of 45 and a standard deviation of eight. Samples of size $n=30$are drawn randomly from the population. Find the probability that the sample mean is between $42$ and $50$.

Based on data from the National Health Survey, women between the ages of $18$and $24$have an average systolic blood pressures (in mm Hg) of $114.8$with a standard deviation of $13.1$. Systolic blood pressure for women between the ages of $18$to $24$follow a normal distribution.

a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than $120.$

b. If$40$women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than $120$.

c. If the sample were four women between the ages of$18$to $24$ and we did not know the original distribution, could the central limit theorem be used?

According to Boeing data, the $757$airliner carries $200$passengers and has doors with a height of $72$inches. Assume for a certain population of men we have a mean height of $69.0$inches and a standard deviation of $2.8$ inches.
a. What doorway height would allow $95\%$of men to enter the aircraft without bending?
b. Assume that half of the $200$passengers are men. What mean doorway height satisfies the condition that there is a$0.95$probability that this height is greater than the mean height of $100$men?

c. For engineers designing the $757$ , which result is more relevant: the height from part a or part b? Why?

The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.

The mean number of minutes for app engagement by a table use is $8.2$ minutes. Suppose the standard deviation is one minute. Take a sample size of $70$.

a. What is the probability that the sum of the sample is between seven hours and ten hours? What does this mean in context of the problem?

b. Find the $84th$and $16th$percentiles for the sum of the sample. Interpret these values in context.

Suppose that the duration of a particular type of criminal trial is known to have a mean of $21$days and a standard deviation of seven days. We randomly sample nine trials.

a. In words,$\mathrm{Î\pounds }X=\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b.$\mathrm{Î\pounds }X~\_\_\_\_\_(\_\_\_\_\_,\_\_\_\_\_)$

c. Find the probability that the total length of the nine trials is at least $225$days.

d. Ninety percent of the total of nine of these types of trials will last at least how long?

74. Suppose that the weight of open boxes of cereal in a home with children is uniformly distributed from two to six pounds with a mean of four pounds and a standard deviation of 1.1547. We randomly survey 64 homes with children.

a. In words, X=

b. The distribution is

c. In words, $∑x$=

d. $∑x~$

e. Find the probability that the total weight of open boxes is less than 250 pounds.

f. Find the$35th$percentile for the total weight of open boxes of cereal.