0.1 Review exercises (ch 3-13)  (Page 8/12)

Use the following information to answer the next three exercises: A group of students measured the lengths of all the carrots in a five-pound bag of baby carrots. They calculated the average length of baby carrots to be 2.0 inches with a standard deviation of 0.25 inches. Suppose we randomly survey 16 five-pound bags of baby carrots.

94. State the approximate distribution for $\overline{X}$ , the distribution for the average lengths of baby carrots in 16 five-pound bags. $\overline{X}$ ~ ______

95. Explain why we cannot find the probability that one individual randomly chosen carrot is greater than 2.25 inches.

96. Find the probability that $\overline{x}$ is between two and 2.25 inches.

Use the following information to answer the next three exercises: At the beginning of the term, the amount of time a student waits in line at the campus store is normally distributed with a mean of five minutes and a standard deviation of two minutes.

97. Find the 90 ^th percentile of waiting time in minutes.

98. Find the median waiting time for one student.

99. Find the probability that the average waiting time for 40 students is at least 4.5 minutes.

Chapter 11

Use the following information to answer the next four exercises: Suppose that the time that owners keep their cars (purchased new) is normally distributed with a mean of seven years and a standard deviation of two years. We are interested in how long an individual keeps his car (purchased new). Our population is people who buy their cars new.

100. Sixty percent of individuals keep their cars at most how many years?

101. Suppose that we randomly survey one person. Find the probability that person keeps his or her car less than 2.5 years.

102. If we are to pick individuals ten at a time, find the distribution for the mean car length ownership.

103. If we are to pick ten individuals, find the probability that the sum of their ownership time is more than 55 years.

104. For which distribution is the median not equal to the mean?

1. Uniform
2. Exponential
3. Normal
4. Student t

105. Compare the standard normal distribution to the Student’s t -distribution, centered at zero. Explain which of the following are true and which are false.

1. As the number surveyed increases, the area to the left of –1 for the Student’s t -distribution approaches the area for the standard normal distribution.
2. As the degrees of freedom decrease, the graph of the Student’s t -distribution looks more like the graph of the standard normal distribution.
3. If the number surveyed is 15, the normal distribution should never be used.

Use the following information to answer the next five exercises: We are interested in the checking account balance of twenty-year-old college students. We randomly survey 16 twenty-year-old college students. We obtain a sample mean of $640 and a sample standard deviation of $150. Let X = checking account balance of an individual twenty year old college student.

106. Explain why we cannot determine the distribution of X .

107. If you were to create a confidence interval or perform a hypothesis test for the population mean checking account balance of twenty-year-old college students, what distribution would you use?