Math 12

Chapters 6-9 Worksheet

Read each question carefully and follow all instructions exactly. Correct answers without adequate supporting work will not receive full credit, so show work whenever possible. It is likely that you will do some work using commands on your graphing calculator. When you do, write a brief description of what you did like “data in L1, 1-Var Stat”.

Put all work and answers in the indicated spaces on the answer sheet provided. Be sure your final answer is clear (boxed or circled). When graphing USE A RULER!

1. The probability distribution below shows the number of people (X) waiting in line at Candi’s Coffee Café at 9am on any given weekday.

X	0	1	2	3	4	5	6	7	8	9
P(X)	0.03	0.07	0.09	0.15	0.08	0.18	0.22	0.11	0.06	0.01

 

 

1. Find P(X=5)
2. Find P(X<5)
3. Based on this data, if you walked into Candi’s Coffee Café at 9am tomorrow, how many people would you expect to see standing in line?

1. According to data collected, 0.6% of Facebook users are under 13 (the site is restricted to users 13 and older). In a simple random sample of 500 children under the age of 13, find the mean and standard deviation for number of Facebook users.

3. A survey found that 80% of US household do some online banking. In a collection of 220 US households, what’s the probability that:

 

1. Exactly 175 do some online banking?
2. Less than 175 do some online banking?
3. 175 or more do some online banking?

1. For each of the following, first draw a standard normal distribution curve and shade the area that corresponds to the probability then find the following probability:

2. P(0<z<2.27)
   b. P(z < -2.05)
   c. P(-1.13 < z < 2.34)

1. Draw a standard normal distribution. Draw a vertical line on your standard normal curve that splits the area under the curve into two parts with an area of 0.9 to the left of the line and an area of 0.1 to the right of the line. What z-score (on the horizontal axis) corresponds to the line you drew?

6. If X is normally distributed with 𝜇 = 12 𝑎𝑛𝑑 𝜎 = 2.5
   Find the area under the normal curve to the left of X = 8.4
7. What two X-values cut out the middle 70% of the area under the normal curve?
8. Scores on the SAT college entrance test in a recent year were approximately normal with 𝜇 =1026 and 𝜎 =209.

1. 1. What’s the probability that a randomly selected test taker scored 1250 or more?
   2. One prestigious college only considers applicants who score in the top 2.5% on the

SAT, what’s the minimum score a test taker needed to earn to be considered by this college?

8. The amount of active ingredient in any single tablet of medicine Z is normally distributed with 𝜇 =50mg and 𝜎 = 0.037mg. Patients experience a dangerous side effect more often if they ingest more than 50.5mg of the active ingredient. What’s the probability that a randomly selected tablet will contain more than 50.5mg of the active ingredient?

 

9. For children in a certain age range, heights are normally distributed with a mean of 25 inches and a standard deviation of 2.1 inches. If one child in this age range is selected at random, what’s the probability that:
10. He/she will be over 27 inches tall?
    b. He/she will be under 23 inches tall?
    c. He/she will be between 24.5 and 25.5 inches tall?
11.   The life of a particular light bulb is normally distributed with a mean of        12,000 hours and a standard deviation of 220 hours.
12. What is the probability that a randomly selected light bulb will last more than 12,500 hours?

1. What is the probability that a random sample of 50 light bulbs will have a mean life of more than 12,500 hours?

11. A sample of 80 eighteen year old women was taken. This sample of women had an average height of 64 inches with a standard deviation of 1.5 inches. Find the 95% confidence interval for the true mean height of eighteen year old women.
12. When 650 college students were surveyed, 495 said they owned a computer. Construct a 98% confidence interval for the proportion of college students who own a computer.
13. A simple random sample of textbooks in a local college bookstore yielded a mean textbook cost of $74.80 with a standard deviation of $19.79. Find an 85% confidence interval for the true mean cost of a college textbook.
14. The heights of a random sample of 38 male officers from a large-city police force were measured. The standard deviation for the sample was 1.83 inches. Find a 95% confidence interval for the standard deviation of the heights of the officers. Heights of men are known to be normally distributed.
15. In a study of 200 accidents that required treatment in an emergency room, 40% occurred at home. Find a 90% confidence interval for the true proportion of accidents that occur at home.

Bonus:  Lucy’s statistics professor asked, “Approximately 43% of marriages in the US end in divorce within 15 years. If I take random sample of 40 couples married in June of 2014, what is the probability that half of them will be divorced by June of 2029?”.Explain how Lucy knows this is a binomial probability problem.