4. If Z is a standard normal random variable, that is Z ∼ N(0, 1), (a) what is P(Z 2 < 1)? (b) Find a number c such that P(Z < c) = 0.75 (c) Find a number d such that P(Z > d) = 0.83 (d) Find a number b such that P(−b < Z < b) = 0.95

Nick paid off a $15,000 car loan over 3 years with monthly payments of $466.59 each. Find the finance charge and the APR.

Use the internet to find a data set. Key terms to search: Free Public Data Sets and Medical Data Sets.

1. Introduce your Data Set and Cite the Source.
2. Why was this data interesting to you?
3. Calculate measures of central tendency (Mean, Median & Mode) and measures of variation (Range and Standard Deviation) for your data. Write a sentence for each calculation explaining what that value means in context of your data.

The “cold start ignition time” of an automobile engine is investigated by a gasoline manufacturer. The following 8 times (in seconds) were obtained for a test vehicle:

1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, 1.91

A Construct and interpret the 95% confidence interval for the population mean start ignition time of an automobile engine.

B Test at 0.05 significance level whether the population mean start ignition time is below 2.9 
seconds. Include the hypotheses, the test st atistic, the p-value, test decision 
and conclusion in the context of the problem.

C. Does the confidence interval in the output support your statistical decision? Explain.

D. Construct a Normal Probability Plot of the data. In your opinion, does the graph support an assumption of normality? Explain.

E. Perform a Shapiro-Wilk test of normality. State hypothesis, p-value and conclusion. Did this support your decision in part (d) based on the normality plot?

F. What test decision error could you have made and provide an explanation of this error in context of the problem.

G. Include a copy of your R-code, test output, and normal probability plot.

1) Every night there is a 20% chance that Mrs. Lemonde will let Mr.Lemonde’s dog George sleep in the bed. Using binomial distributions answer the following:

a) What is the probability that George sleeps with Mr. Lemonde exactly twice in one week? Explain

b) What is the probability that George sleeps with Mr. Lemonde at least once in one week?

1: A survey questioned 1,000 high school students. The survey revealed that 46% are honor roll students. Of those who are honor roll students, 45% play sports in school and 21% of those that are not honor roll students, don't play sports. What is the probability that a high school student selected at random plays sports in school?

2: One of two small classrooms is chosen at random with equally likely probability, and then a student is chosen at random from the chosen classroom. Classroom #1 has 5 boys and 11 girls. Classroom #2 has 14 boys and 9 girls. What is the probability that Classroom #2 was chosen at random, given that a girl was chosen? Your answers should be rounded to 4 digits after the decimal.

#1) 68% of all Americans are home owners. If 46 Americans are randomly selected, find the probability that a. Exactly 32 of them are are home owners. b. At most 32 of them are are home owners. c. At least 32 of them are home owners. d. Between 25 and 33 (including 25 and 33) of them are home owners.

#2) 31% of all college students major in STEM (Science, Technology, Engineering, and Math). If 32 college students are randomly selected, find the probability that

a. Exactly 9 of them major in STEM.  
b. At most 10 of them major in STEM.  
c. At least 10 of them major in STEM.  
d. Between 6 and 13 (including 6 and 13) of them major in STEM.

#3)

56% of all violent felons in the prison system are repeat offenders. If 50 violent felons are randomly selected, find the probability that  

a. Exactly 29 of them are repeat offenders.
b. At most 30 of them are repeat offenders.
c. At least 25 of them are repeat offenders.  
d. Between 25 and 30 (including 25 and 30) of them are repeat offenders.

#4) 63% of all Americans live in cities with population greater than 100,000 people. If 49 Americans are randomly selected, find the probability that

a. Exactly 28 of them live in cities with population greater than 100,000 people.  
b. At most 29 of them live in cities with population greater than 100,000 people.
c. At least 30 of them live in cities with population greater than 100,000 people.  
d. Between 25 and 32 (including 25 and 32) of them live in cities with population greater than 100,000 people.

According to a marketing website, adults in a certain country average 61 minutes per day on mobile devices this year. Assume that minutes per day on mobile devices follow the normal distribution and has a standard deviation of 11 minutes. Complete parts a through d below.

a. What is the probability that the amount of time spent today on mobile devices by an adult is less than 70

minutes?

(Round to four decimal places as needed.)

b. What is the probability that the amount of time spent today on mobile devices by an adult is more than 50

minutes?

(Round to four decimal places as needed.)

c. What is the probability that the amount of time spent today on mobile devices by an adult is between 40and 56

minutes?

(Round to four decimal places as needed.)

d. What amount of time spent today on mobile devices by an adult represents the 60th percentile?

An amount of time of minutes represents the 60th percentile.

1 The Earth is structured in layers: crust, mantle, and core. A recent study was conducted to estimate the mean depth of the upper mantle in a specific farming region in California. Twenty-six, n = 26 sample sites were selected at random from a normally distributed population of approximately N = 1598 sites, and the depth of the upper mantle was measured using changes in seismic velocity and density. The sample mean was 127.5 km and the sample standard deviation was 21.3 km. Suppose the depth of the upper mantle is normally distributed. Find a 90% confidence interval for the true mean depth of the upper mantle in this farming region.

1. Determine the prerequisites have been met (3 pts):

• Random sample:
• n ≤ 0.05 of N:
• the population is normally distributed or n ≤ 30:

2. Construct the confidence interval (4 pts):

3. Interpret the confidence interval, in a statement (1 pt):

A program was created to randomly choose customers at a shoe store to receive a discount. The program claims 15% of the receipts will get a discount in the long run. The manager of the shoe store is skeptical and believes the program's calculations are incorrect. She selects a random sample and finds that 12% received the discount. The confidence interval is 0.12 ± 0.05 with all conditions for inference met.

Part A: Using the given confidence interval, is it statistically evident that the program is not working? Explain.

Part B: Is it statistically evident from the confidence interval that the program creates the discount with a 0.15 probability? Explain.

Part C: Another random sample of receipts is taken. This sample is six times the size of the original. Twelve percent of the receipts in the second sample received the discount. What is the value of margin of error based on the second sample with the same confidence level as the original interval?

Part D: Using the margin of error from the second sample in part C, is the program working as planned? Explain.

Assume that military aircraft use ejection seats designed for men weighing between

149.6149.6

lb and

212212

lb. If​ women's weights are normally distributed with a mean of

177.2177.2

lb and a standard deviation of

48.748.7

​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

The percentage of women that have weights between those limits is

nothing​%.

​(Round to two decimal places as​ needed.)

1. What percentage of data would you predict would be between 25 and 50 and what percentage would you predict would be more than 50 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 25 and 50 as well as for more than 50. Now determine the percentage of data points in the dataset that fall within each of these ranges, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?

DRIVE:

Find c such that each of the following is true. (Round your answers to two decimal places.)

(a)    p(0 < z < c) = 0.1349
c =

(b)    p(c < z < 0) = 0.4845
c =

(c)    p(−c < z < c) = 0.4640
c =

(d)    p(z > c) = 0.6075
c =

(e)    p(z > c) = 0.0531
c =

(f)    p(z < c) = 0.1003

QUESTION 7    [18 MARKS)

In the following table, optimistic, most likely and pessimistic time estimates have been given for each activity for a project.

1. Construct an activity on node network diagram for this project.                               
2. If the project is due to be completed in 47 days, what is the probability that this project will be completed on or before the due date?                                                                
3. If the project manager wants at least a 95% probability that the project will be completed on or before the due date, what is the shortest project time due date that will satisfy the manager?