1- Assume thatwomen's heights are normally distributed with a mean given by =64.3in, and a standard deviation given by =2.3in. If 39 women are randomlyselected, find the probability that they have a mean height less than 65 in. The probability is approximately, (Round to four decimal places asneeded.)

2- The overhead reach distances of adult females are normally distributed with a mean of 197.5cm and a standard deviation of 8.3cm. Find the probability that the mean for 25 randomly selected distances is greater than 196.00 cm. The probability is ? (Round to four decimal places asneeded.)

3-Use the sample data and confidence level given below.

A research institute poll asked respondents if they felt vulnerable to identity theft. In thepoll, n= 913 and x=555 who said"yes." Use a 95% confidence level. Identify the value of the margin of error E.

4- A drug is used to help prevent blood clots in certain patients. In clinicaltrials, among 4153 patients treated with thedrug, 133developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions. Construct the confidence interval.

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5- A data set includes 108 body temperatures of healthy adult humans having a mean of 98.3F and a standard deviation of 0.69F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What is the confidence interval estimate of the population mean ? (Round to three decimal places asneeded.)

( ) F < < ( ) F

6- An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 8 IQ points of the true mean. Assume that =18 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is ? (Round up to the nearestinteger.)