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Statistics – Chapters 6 & 7 – Normal & Sampling Distributions – Study Guide
1. What is the difference between a continuous and discrete random variable?
2. What is the difference between the binomial distribution and the normal distribution?
3. What is the difference between a normal distribution and a standard normal distribution?
4. What is a sampling distribution?
5. What is the standard deviation?
6. What is a x value? What is a z-score?
7. Draw and label the empirical rule.
8. What is theorem 7.1? What is the central limit theorem?
9. Use the empirical rule to solve the following problem. Mr. Keenan’s chapter 6 & 7 test traditionally has a mean value of 83 with a standard deviation of 4 points.
a. What is the probability that someone will score greater than an 83?
b. What is the probability that someone will score less than a 75?
c. What is the probability that someone will score between 75 and 95?
d. What is the probability that someone will score between 79 and 87?
e. What is the probability that someone will score between 75 and 91?
f. What it the probability that someone will score between 71 and 95?
10. Kristina is opening up a restaurant in downtown Boston. According to her records for the first month she should sell an average of 42 meals a day, with a standard deviation of 4 meals.
a. How many meals correspond with z scores of 1.43 and -2.65?
b. Find the probability that Kristina will sell less than 39 meals.
c. Find the probability that Kristina will sell more than 47 meals.
d. Find the probability that Kristina will sell between 30 and 50 meals.
e. Find the probability that Kristina will sell more than 35 meals, but less that 52.
11. Kristina is opening up a restaurant in downtown Boston. According to her records for the first month she should sell an average of 42 meals a day, with a standard deviation of 4 meals.
a. Kristina only wants to refund money for the bottom 8%, how many meals is she going to give away?
b. How many meals contain 92% of Kristina’s sales (centered about the mean)?
c. If an employee sells enough meals to be in the top 5% of the number meals sold, then he will win $50.00. How many meals does he have to sell in order to be in the top 5%?
12. The newly elected President is flying all over the United States for meetings and speeches. The probability that the President will fly is .60 on any given day in a traditional month of 30 days.
a. Find the probability that the President will fly less than 20 days.
b. Find the probability that the President will fly between 25 and 30 days.
c. Find the probability that the president will fly l0 or more days.
13. Stuart has observed that the daily revenues from his coffee house follow an approximately normal distribution with mean of $550 and standard deviation $175.
a. Find the probability that the revenues for a day chosen at random will be between $500 and $600.
b. Find the probability that the sample mean revenues for a random sample of 7 days will be between $500 and $600.
c. Find the probability that the sample mean revenue for a random sample of 25 days will be less than $500.
d. Find the probability that the sample mean revenue for a random sample of 36 days will be more than $600.
14. A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 72% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. On a certain day, six customers bought it.
a. Find the probability that three people will like it.
b. Find the probability that less than three people will like it.
15. Below is the number of times the President traveled using Air Force One per month for 15 consecutive months. From past records, he flies an average of 18 times a month, with a standard deviation of 3. Make a control chart to determine if the President’s habits are out of control. Should congress restrict his flying? Explain your answer.
Months / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15# of flights / 10 / 18 / 25 / 23 / 26 / 22 / 15 / 24 / 18 / 29 / 17 / 16 / 28 / 13 / 18
Statistics – Chapter 6 & 7 – Normal Distributions – Study Guide – Answers
1. A continuous random variable takes on a infinite number of values; whereas, a discrete random variable takes on a finite number of values.
2. A binomial distribution graphs a discrete random variable (r) and a normal distribution graphs a continuous random variable (x).
3. A normal distribution graphs raw data (x) and a standard normal distribution graphs z-scores (z).
4. A sampling distribution is a probability distribution for a sample statistic.
5. Standard deviation is the average distance away from the mean.
6. X values are raw data. Z-scores are the number of standard deviations away from the mean.
7. Look on page 276
8. Look in notes.
9a.
9b.
9c.
9d.
9e.
9f.
10a.
10b.
10c.
10d. 9
10e.
11a. or about 36 meals
11b. from 35 to 49 meals
11c. or about 49 meals
12a.
12b.
12c.
13a.
13b.
13c.
13d.
14a. P(r = 3) = .164
14b. P(r < 3) = P(r = 0) + P(r = 1) + P( r = 2) = .048 + .007 + .000 = .055
15. Out of Control: Signals I & III