(b) Identify two population parameters that she would be likely to estimate for her study.

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1 1. Bethany wants to study the number of people who visit the Denver Zoo each day in a given year. The zoo is open and accessible year round. (a) Describe the population for this study. (b) Identify two population parameters that she would be likely to estimate for her study. (c) What statistics could she use to estimate these parameters? ans; 2. Which of the following variables does NOT signify a population parameter? A) B) C) D) E) 3. Which of the following variables does NOT signify a sample statistic? A) B) C) D) E) 4. At Disney World, Jesse, one of the attendants, has been measuring the time a tourist waits in line for Space Mountain. Over a long period of time the attendant has found the mean waiting time to be 49 minutes with standard deviation 12 minutes. (a) What is the probability that a random sample of 38 tourists will have a sample mean waiting time of 52 or more minutes? (b) What is the probability that a random sample of 77 tourists will have a sample mean waiting time of less than 45 minutes?

2 Untitled1.notebook February 20, The heights of 18 year old men are normally distributed, with a mean inches and standard deviation inches. (a) What is the probability that one 18 year old man selected at random will be less than 67 inches tall? (b) What is the probability that a random sample of nine 18 year old men will have a mean height of less than 67 inches?

3 Untitled1.notebook February 20, According to a large survey, 38% of teenagers think it is more important to take debate than it is to take math. Suppose we have a group of 40 random teenagers. We will ask them if they think it is more important to take debate than math. a) Can we approximate p by a normal distribution? Explain. b) Find continuity correction c) Compute P(.30 < p <.40). d) compute P(p >.5)

4 7. A sociology course is taught each semester. The course always fill up to its maximum of 60 students. A P Chart is to be made for the proportion of A s given in the course each semester for the past 14 semesters. Each student is viewed as a binomial trial. Success means the student got an A, and failure is not getting an A. Since the class size is 60 each semester, the number of trials is n = 60. Using information from the registrar s office, the following data is obtained. semester r = number of A's r/ semester r = number of A's r/ (a) Make a P chart showing the proportion of A s. (b)determine whether the proportion of A s is in statistical control. If it is not, specify which out ofcontrol signals are present. 1. If 9 consecutive points are on one side of the p 2. If you find 3 consecutive points on the same side of the mean and at least 2 of the 3 are beyond the second standard deviation. 3. Any point beyond the 3rd standard deviation 8. Life spans for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years. a) find the probability that a red fox chosen at random will live at least 10 years. b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.

5 8. Suppose we have a binomial distribution with trials and probability of success. The random variable is the number of successes in the 35 trials, and the random variable representing the proportion of successes is. Note: Approximate all values except z values to three decimal places. n = p = q = np = nq = Continuity correction (a) find (b) find 9. The general manager of an amusement park wants to estimate the length of time people spend in the park. From data collected over several months it was found that the average time an individual spends in the park is 3.4 hours. with a standard deviation of 1.1 hours. It was not known whether the distribution is normal but it appears to be mound shaped. a) Thirty five people just got off the city bus and went into the amusement park. Find the probability that the sample mean time these people spend in the park is more than 3 hours. b) Find the probability that the sample mean time these people spend in the park is between 3 hr. and 3.5 hr.

6 Test tomorrow, 3 x 5 note card allowed MEASURE IT! allowed to write on the front and back. Must be written in your own handwriting. No printed / copied information allowed. Important things to know for the test. To use the standard normal distribution to approximate a sample mean distribution at least one of the following conditions must be met: 1. the original distribution must be normal 2. the sample size must be > 30 To use the standard normal distribution to approximate for a sample proportion both, np > 5 and nq > 5 Population parameters include: Sample statistics include: For sample mean distributions we change to 'z' using: Then shade in the bell and use the charts to find how much is shaded. For sample proportions, find: the mean, standard deviation and continuity correction. Change to 'x' by adding or subtracting continuity correction Change 'x' to 'z' by using: Then shade in the bell and use the charts to find how much is shaded. To find To find To find P charts average the sample proportion numbers. do use Know the 3 out of control signals to watch for 1. If 9 consecutive points are on one side of the p 2. If you find 3 consecutive points on the same side of the mean and at least 2 of the 3 are beyond the second standard deviation. 3. Any point beyond the 3rd standard deviation