Provide an appropriate response. (Show steps to get maximum points)
1) Test scores for a statistics claw had a mean of 79 with a standard deviation of 4.5. Test scores for a calculus class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 83 on the statistics test and a 95 on the calculus test. Calculate the z-score for each test. On which test did the student perform better relative to the other students in each class?
2) Many firms use on-the-job training to teach their employees new software. Suppose you work in the personnel department of a firm that just finished training a group of its employees in new software, and you have been requested to review the performance of one of the Trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 74 and 5, respectively, and the distribution of scores is mound-shaped and symmetric Suppose the trainee in question received a score of 58. Compute the trainees z-score.
3) A highly selective boarding school will only admit students who place at least 1.5 a-scores above the mean on a standardized test that has a mean of 110 and a standard deviation of 12. What is the minimum score that an applicant must make on the test to be accepted?
Answer the question.
(Give a reason for your answer)
4) Focus groups of 11 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 7.8, and the standard deviation is 0.97. Would it be unusual to randomly select 11 people and fmd that fewer than 4 recognize the Yummy brand name?
5) Focus groups of 14 people are randomly selected to discuss products of the Famous Company. It is determined that the mean number (per group) who recognize the Famous brand name is 9, and the standard deviation is 0.79. Would it be unusual to randomly select 14 people and find that greater than 13 recognize the Famous brand name?
6) Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. is it unusual for a team to win a series in 5 games?
Provide an appropriate response.
7) Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follow.
68 73 66 76 86 74 61 89 65 90 69 92 76
62 81 63 68 81 70 73 60 87 75 64 82
Find
1) Ql of the data.
2) The 28th percentile of the data (P2g)
3) The 65th percentile of the data (1.65)
8) Eleven high school teachers were asked to give the numbers of students in their classes. The sample data follow. 36, 31, 30, 31, 20, 19, 24, 34, 21, 28, 24. Find the five-number summary and draw the box plot if the data. ( 15 points. 5 points are for the plot itself. Show full steps to get maximum points)
9) The following is a sample of 19 November utility bills (in dollars) from a neighborhood.VVhat is the largest bill in the sample that would not be considered an outlier? ( 7 points . Show steps to get maximum points) 52, 62, 66, 68, 72, 74, 76, 76, 76, 78, 78, 82, 84, 84, 86, 88, 92, 96, 110
Use the Emperical Rule to .ohre(#io,m, n2) and Chabychev's inequality(413, 414) to solve the following.( 6 points each)
10) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 16 and 5, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a bell-shaped distribution. Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distrilmtion.
11) The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution of the scores is roughly bell shaped. Use the Empirical Rule to find the percentage of scores that lie between 60 and 80.
12) The scores from a state standardized test have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical Rule to find the percentage of students with scores between 70 and 130.
13) At a tennis tournament a statistician keeps track of every serve. The statistidart reported that the mean serve speed of a particular player was 98 miles per hour (mph) and the standard deviation of the serve speeds was 14 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.
14) A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 400 with a standard deviation of 50 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 300 and 500?
Provide an appropriate response.
15) Given the table of probabilities for the random variable x, does this form a probability distribution?
x 5 10 15 20
P(x) 0.10 -0,30 0.50 0.70
16) Given the table of probabilities for the random variable x, does this form a probability distribution?
|
x
|
0
|
1
|
2
|
3
|
4
|
|
P(x)
|
0.02
|
0.07
|
0.22
|
027
|
0.42
|
17) Consider the discrete probability distribution to the right when answering the following question. Find the probability that x equals 4.
x 2 4 7 8
P(x) 0.25 ? 0.22 026
Provide an appropriate response.
18) The produce manager at a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x apples.
Find
1. the mean number of oranges purchased by a customer.
2. the variance of the number of oranges purchased.
3. Standard deviation of oranges purchased.
x 1 2 3 4 5 6 7 9 10
p(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0.01
19) A lab orders a shipment of 100 rats a week 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below:
Price $10.00 $12.50 $15.00
Probability 0.45 0.2 0.35
How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.)
Use the Poisson Distribution to find the indicated probability.
20) If the random variable x has a Poisson Distribution with mean p= 6, find the probability that x = 2.
21) A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.8. Find the probability that on a randomly selected trip, the number of whales seen is 4.
22) In one town, the number of burglaries in a week has a Poisson distribution with a mean of 4.6. Find the probability that in a randomly selected week the number of burglaries is at least three.
Use the Binomial Distribution to find the indicated probability.
23) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly four girls in ten births.
24) The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime?
25) A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the quiz?
26) According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum?
27) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Suppose that 700 couples each have a baby; find the mean and standard deviation for the number of boys in the 700 babies.
28) A quiz consists of 770 true or false questions. If the student guesses on each question, what is the mean number of correct answers?