Create a histogram on excel for a coin toss. Flip the coin 6 times, each time moving down to the left (for heads) and to the right (for tails).

Consider it a success if when flipping a coin, the coin lands with the head side facing up. Then the probability of a success is .5 (p=.5) and the probability of failure is .5 (q=.5) for each event of flipping a coin. In this lab you will repeat a procedure of 6 events by flipping a coin six time (n=6). And you will record the number of successes (heads) and failures (tails) for each procedure.

My results: 384 coin tosses= 64 rounds

3 rounds resulted in 6 times landing on Heads.

8 rounds resulted in 5 Heads 1 Tail

14 rounds resulted in 4 Heads 2 Tails

20 rounds resulted in 3 Heads 3 Tails

11 rounds resulted in 2 Heads 4 Tails

8 rounds resulted in 1 Head 5 Tails

0 rounds resulted in 6 Tails

I need to create a frequency table for excel, In order to create a histogram.

Using the program R, Assume that the distribution of the duration of human pregnancies can be approximated with a normal distribution with a mean of 266 days and a standard deviation of 16 days.

(a) What percentage of pregnancies should last between 260 and 280 days?

(b) Find a value x such that 10% of the pregnancies of a duration that is longer than x days.

(c) We select 500 pregnant women at random. Let N be the number of pregnancies in the sample with a duration between 260 and 280 days. Compute P(200 ? N ? 300) and P(N = 265).

(d) We select 10 pregnant women at random. What is the probability that the average duration of these 10 pregnancies will be less than 260 days?

(e) We select 60 pregnant women at random. What is the probability that the average duration of these 60 pregnancies will be less than 260 days?

(f) If the duration of a human pregnancy is not normally distributed (in fact it is highly skewed to the left), how does this impact your answers to (d) and (e)? (Explain in words. No computations are necessary for this question.)

1.)

The time college students spend on the internet follows a Normal distribution. At Johnson University, the mean time is 5.5 hours per day with a standard deviation of 1.1 hours per day.

1. If 100 Johnson University students are randomly selected, what is the probability that the average time spent on the internet will be more than 5.8 hours per day?
   Round to 4 places.  
   
2. If 100 Johnson University students are randomly selected, what is the probability that the average time spent on the internet is between 5.3 hour and 5.8 hours?
   Round to 4 places  
   
3. If 100 Johnson University students are randomly selected, what mean number of hours on the internet per day separated the bottom 33% and top 67% of internet usage for college students?  
   hours per day. Round to 2 places.

2.)

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.1 years, and standard deviation of 0.5 years.

If 19 items are picked at random, 3% of the time their mean life will be less than how many years?

Give your answer to one decimal place.

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean μ = 843 grams and standard deviation of σ = 8 grams.

(a) Describe the distribution of x, the amount of fill per jar.

1) skewed right

2) normal    

3) skewed left

4) chi-square

_

(b) Find the probability that one jar selected at random contains between 835 and 865 grams. (Give your answer correct to four decimal places.)

_

(c) Describe the distribution of x, the mean weight for a sample of 20 such jars of sauce.

1) skewed right

2) normal

3) skewed left

4) chi-square

_

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)


(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)


(e) Find the probability that a random sample of 20 jars has a mean weight between 835 and 865 grams. (Give your answer correct to four decimal places.)

Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 60 percent and the probability of a recession is 40 percent. It is projected that the company will generate a total cash flow of $205 million in a boom year and $96 million in a recession. The company's required debt payment at the end of the year is $130 million. The market value of the company’s outstanding debt is $103 million. The company pays no taxes.

a. What payoff do bondholders expect to receive in the event of a recession? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) Calculate Payoff $

b. What is the promised return on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Promised return % c. What is the expected return on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Calculate Expected return %

A company wants to determine if the median shelf life for their product is different from the median shelf life of their main competitor’s product. Their main competitor’s product has a median shelf life of 10 days. Since the product is very expensive, the company only wants to devote a small number of units to the associated test. They test 7 units of product and find the following results.

a) What type of hypothesis test should you conduct in this case?

b) Conduct your chosen hypothesis test using the p-value method. Show all 5 steps. When you calculate your test statistic: show the equation you use, how you plug in, and your final answer. When you calculate your p-value: show how you calculate each individual probability, and round each individual probability to 4 decimal places.

1. Unrelated to the problems above, --If as a result of an ANOVA test of the difference between three different pain relievers, you cannot prove a difference for alpha=.05, what is the probability that you would reach this conclusion if , in fact, there was a difference?

Group of answer choices

a) .95

b) small if the sample size is small

C) alpha

D) small if the diets make a big difference

e) it depends on your p value

2. If as a result of an ANOVA test you reject the null hypothesis, you know

A) the means may all be the same

B) the means are all the same

C) all the means are different

D) a majority of the means are different from each other

E) at least one of the means differs from at least one other

3. You use ANOVA to see if people in different countries sleep a different number of hours on average. What is the probability you would find a difference if no difference existed?

A) alpha

B) 1- beta

C) beta

D) 1- alpha

E ) it depends on how much of a difference there really is

2. [12 marks] A company wants to determine if the median shelf life for their product is different from the median shelf life of their main competitor’s product. Their main competitor’s product has a median shelf life of 10 days. Since the product is very expensive, the company only wants to devote a small number of units to the associated test. They test 7 units of product and find the following results.

a) What type of hypothesis test should you conduct in this case? [1 mark]

b) Conduct your chosen hypothesis test using the p-value method. Show all 5 steps. When you calculate your test statistic: show the equation you use, how you plug in, and your final answer. When you calculate your p-value: show how you calculate each individual probability, and round each individual probability to 4 decimal places. [11 marks]

With a town of 20 people, 2 have a certain disease that spreads as follows: Contacts between two members of the town occurred in accordance with a Poisson process having rate ?. When contact occurs, it is equally likely to involve any of the possible pairs of people in the town. If a diseased and non-diseased person interect, then, with probability p the non-diseased person becomes diseased. Once infected, a person remains infected throughout. Let ?(?) denote the number of diseased people of the town at time t. Considering the current time as t = 0, we want to model this process as a continuous-time Markov chain.

(a) What is the state space of this process?

(b) What is the probability that a diseased person contacts a non-diseased person?

(c) What is the rate at which a diseased person contacts a non-diseased person (we denoted this type of contact by I-N contact) when there are X diseased people in the town?

(d) Is the inter-contact time between two I-N contacts exponentially distributed? Why?

(e) Compute the expected time until all people of the town are infected by the disease.

Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 80 percent and the probability of a recession is 20 percent. It is projected that the company will generate a total cash flow of $194 million in a boom year and $85 million in a recession. The company's required debt payment at the end of the year is $119 million. The market value of the company’s outstanding debt is $92 million. The company pays no taxes.