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If a \( z \)-score is zero, which of the following must be true? Explain your reasoning. - The mean is zero. - The corresponding \( x \)-value is zero. A. The corresponding \( x \)-value is equal to the mean. divided by the standard deviation. B. The mean is zero, because the mean is always equal to the \( z \)-score. C. The corresponding \( x \)-value is zero, because the \( z \)-score is equal to the \( x \)-value divided by the standard deviation.

In a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is (b) Find the probability that a study participant has a height that is between 67 and 70 inches. The probability that the study participant selected at random is between 67 and 70 inches tall is \( \square \). (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 70 inches. The probability that the study participant selected at random is more than 70 inches tall is \( \square \). (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 . The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . C. There are no unusual events because all the probabilities are greater than 0.05. D. The event in part (a) is unusual because its probability is less than 0.05 .

\( 1 \leftarrow \begin{array}{l}\text { A vending machine dispenses coffee into a twenty-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard } \\ \text { deviation of } 0.01 \text { ounce. You can allow the cup to overfill } 4 \% \text { of the time. What amount should you set as the mean amount of coffee to } \\ \text { be dispensed? } \\ \text { Click to view page } 1 \text { of the table Click to view page } 2 \text { of the table. } \\ \square \text { ounces } \\ \text { (Round to two decimal places as needed.) }\end{array} \).

\( \leqslant \) What is the total area under the normal curve? Choose the correct answer below. A. It depends on the mean. B. 1 C. It depends on the standard deviation. D. 0.5

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. As the size of a sample increases, the mean of the distribution of sample means increases. Choose the correct answer below. A. False. As the size of a sample increases, the mean of the distribution of sample means decreases. C. True. D. False. The mean of a distribution of sample means changes independently of the corresponding sample size.

What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution? Choose the correct answer below. A. The mean and standard deviation have the values of \( \mu=0 \) and \( \sigma=1 \). The mean and standard deviation have the values of \( \mu=1 \) and \( \sigma=1 \). The mean and standard deviation have the values of \( \mu=1 \) and \( \sigma=0 \). D. The mean and standard deviation have the values of \( \mu=0 \) and \( \sigma=0 \).

A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that \( 69 \% \) have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the past 12 months. Select the correct answer below and, if necessary, fill in the answer boxes within your choice. A. No, because \( \mathrm{np}<5 \). No, because nq <5. C. Yes, the mean is \( \square \) and the standard deviation is (Round to two decimal places as needed.)

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution of a sample mean is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution of a sample mean is approximately normal if either \( \mathrm{n} \geq 30 \) or the population is normal. B. The statement is false. A sampling distribution of a sample mean is approximately normal only if \( \mathrm{n} \geq 30 \). C. The statement is false. A sampling distribution of a sample mean is never normal. D. The statement is true.

The sample size \( n \), probability of success \( p \), and probability of failure \( q \) are given for a binomial experiment. Decide whether you can use a normal distribution to approximate the distribution of \( x \). \( n=20, p=0.89, q=0.11 \) Can a normal distribution be used to approximate the distribution of \( x \) ? A. No, because \( n q<5 \). B. No, because \( n p<5 \) and \( n q<5 \). C. No, because \( n p<5 \). D. Yes, because \( n p \geq 5 \) and \( n q \geq 5 \).

In a survey of 18 -year-old males, the mean weight was 170.3 pounds with a standard deviation of 46.2 pounds. Assume the distribution can be approximated by a normal distribution. (a) What weight represents the 95th percentile? (b) What weight represents the 32nd percentile? (c) What weight represents the first quartile? (a) \( \square \) pounds (Round to one decimal place as needed.) (b) \( \square \) pounds. (Round to one decimal place as needed.) (c) \( \square \) pounds. (Round to one decimal place as needed.) (Rs