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The overhead reach distance of adult female are normally distributed with a mean of 197.5 cm and a standard deviation of 8 cm.

Find the probability that an individual distance is greater than 210.90cm.

Find the probability that the mean of 25 random selected distances is greater than 196.00 cm.

Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

**Question:**

Women have head circumferences that are normally distributed with a mean given by u=24.35 in, and a standard deviation given by o = 0.9in.

A. If a hat company produces women’s hates so that they fit head circumferences between 23.6 in and 24.6 in, what is the probability that a randomly selected women will be able to fit into one of these hats?

B. If the company wants to produce hats to fit all women except for those with the smallest 2.5% and Largest 2.5% head circumferences, what head circumferences should be accommodated?

**Question:**

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8591 g and a standard deviation of 0.0516 g. A sample of these candies came from a package containing 459 candies, and the package label stated that the net weight is 391.6 g. (If every package has 459 candies, the mean weight of the candies must exceed 391.6/459 = 0.8532 g for the net contents to weight at least 391.6 g.)

a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g.

the probability is ____? (round to four decimal places)

**Question:**

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighting between 120 lbs and 171 lbs. The new population of pilots has normally distributed weights with a mean of 130 lbs and a standard deviation of 31.2 lbs.

A. If a pilot is randomly selected, find the probability that his weight is between 120 lbs and 171 lbs.

The probability is approximately _________. (Round to four decimal places as needed.).

**Question:**

Express the confidence interval (0.063, 0.149) in the form of p -E< p < p + E.

Asks _____ < p < _____ (Type integers or decimals)

**Question:**

Use the sample data and confidence level given below to complete parts (a) through (d).

A research institute poll ask respondents if they felt vulnerable to identity theft, in the poll, n = 1040, and x = 563 who said “Yes”. Use a 95% confidence level.

A. Find the best point estimate of the population proportion p. ______ (Round to three decimal places as needed).

**Question 7.2.15**

A research institue poll asked respondents if they acted to annoy a bad driver. In the poll, n=2459,

A. Find the best point estimate of the population proportion p. _____ (Round to three decimal places as needed).

**Question 7.2.18**

In the week before and the week after a holiday, there were 13,000 total deaths, and 6487 of them occurred in the week before the holiday.

A. Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday.

B. Based on the results, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?An online site presented this question, “Would the recent norovirus outbreak deter you from taking a cruise? Among 34,009 people who responded, 64% answered “yes”. Use the sample data to construct a 90% confidence interval estimate for the proportion of the population of all people who would respond “Yes” to that question Does the confidence interval provide a good estimate of the population proportion?

_____ < p < _____ (Round to three decimal places as needed).