a) Using the empirical rule, 95% of female promotional customer ages should be between what two values? Either show work or explain how your answer was calculated.

b)Using the empirical rule, 68% of items purchased should be between what two values? Either show work or explain how your answer was calculated.    

1. Consider the table of test scores below:

1. Find the Mean.
2. Find the Median.
3. Find the Mode.
4. Discuss which of these statistics you would use to describe this set of test scores and back up your choice with some reasoning from the book or from your notes.

Consider the following experiment: we roll a fair die twice. The two rolls are independent events. Let’s call M the number of dots in the first roll and N the number of dots in the second roll.

(a) What is the probability that both M and N are even?

(b) What is the probability that M + N is even?

(c) What is the probability that M + N = 5?

(d) We know that M + N = 5. What is the probability that M is an odd number?

(e) We know that M is an odd number. What is the probability that M + N = 5?

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows:

(a) Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary X. (Enter your answers for p(x) as fractions.)

(b) Suppose one of the three offices is randomly selected. Let X₁ and X₂ denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions.)

(c) How does E(X) from parts (a) and (b) compare to the population mean salary μ?

E(X) from part (a) is  _______ μ, and E(X) from part (b) is _______ μ.

The following table shows the length of stay distribution for guests staying at a beach resort, in days. The resort management makes a net profit of $250 per day per guest during the first 2 days of the stay, and $150 per day per guest after the first 2 days. How much profit will the resort owners make in a month (assuming 30 days in a month) if there are 100 guests arriving per day? [Hint: Note that a guest who only stays for two days is billed $500; find the average profit for one guest then work out for the entire month.]

Must be completed in Excel

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 203.21 seconds with a standard deviation of 5.67 seconds. A random sample of 90 times is taken. There is a 51% chance that the average drive-thru service time is less than ________ seconds.

Men at a construction site were moving concrete blocks from a truck, a short distance to the base of a house. The first day the average man moved 62 blocks per hour.

The current day the numbers were : 70,63,76,86,86,62,97,70,77,81

1. Assume all assumptions are met. Provide descriptive statistics for the sample.

2. Conduct a statistical test to assess if the men were able to move more than 62 blocks per hour.

3. The men had more rest than they did the first day and were certain they could move atleast 5 more blocks per hour. Conduct a statistical test to see if they were able to, on average, move 5 more plants per hour than the previous mark of 62

A. Here is a bivariate data set.

Find the correlation coefficient and report it accurate to three decimal places.
r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

B. Based on the data shown below, calculate the correlation coefficient (to three decimal places)

A claim with an alpha =0.10 and a mu of 20. A sample size of 30 yields a sample mean of 17.5 and a sample standard deviation of 10. What is the upper confidence limit with 3 decimal places?

Distillation is a process for separating and collecting substances according to their reaction to heat. When heat is applied to a mixture, the substance that evaporates and is collected as it cools is the distillate. The unevaporated portion of the mixture is the residue. Oil obtained from orange blossoms through distillation is used in perfume. Suppose the oil yield is normally distributed. In a random sample of eleven distillations, the sample mean oil yield was 980.2 grams with sample standard deviation 27.6 grams. If possible, answer (a) to (d). If not possible, explain.

(a) Find the point estimate.

(b) Find the standard error.

(c) Find the margin of error at the 99% confidence level.

(d) Find and interpret the 99% confidence interval.

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 3.0. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance. (a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² ≠ 5.1

H_o: σ² = 5.1; H₁: σ² > 5.1    

H_o: σ² < 5.1; H₁: σ² = 5.1

H_o: σ² = 5.1; H₁: σ² < 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.

We assume a uniform population distribution.    

We assume a binomial population distribution.

We assume a exponential population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.

At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ² lies outside this interval.

We are 90% confident that σ² lies below this interval.    

We are 90% confident that σ² lies within this interval.

We are 90% confident that σ² lies above this interval.

D) Use the normal model to determine the proportion of babies in each class

How do I manually determine the normal mode? Please provide step by step manually (excel is what I am using, however I need to show steps.

Thank you.

6.20. A convenience store owner wants to know how long his customers spend browsing the store before making a purchase. It is found that time spent is normally distributed with an average of m = 5 minutes and a standard deviation of s=2 : 2 minutes. Using a random sample of 14 customers, what is the probability that a customer, on average, will spend less than 4 minutes browsing the store?

1a) Explain why we reject the null hypothesis when the p-value is less than the level of significance?

b) Explain to someone unfamiliar with statistics how to tell whether a statistical test is left, right, or two tailed. Explain what to look for in the wording of a hypothesis test and with the alternate hypothesis.

c) Why can we never truly accept the null hypothesis?