7.9 A company is having a new corporate website developed. In the
final testing phase the download time to open the new home
page is recorded for a large number of computers in office and
home settings. The mean download time for the site is
3.61 seconds. Suppose that the download times for the site are
normally distributed with a standard deviation of 0.5 seconds. If
you select a random sample of 30 download times:
a. What is the probability that the sample mean download time
is less than 3.75 seconds?
b. What is the probability that the sample mean is between
3.70 and 3.90 seconds?
c. The probability is 80% that the sample mean is between
which two values symmetrically distributed around the
population mean?
d. The probability is 90% that the sample mean is less than
what value?

56% of CCBC students are women. Find the probability that in a group of 10 randomly selected CCBC students 6 are women.

2.      Six cards are drawn from an ordinary pack without replacement. Find the probability of getting no spades?

3.      The lengths of arrows in an archery competition follow a normal distribution with mean 26.6 inches and standard deviation 3.5 inches. Find the probability that an arrow is less than 28.0 inches long.

4.      Find the mean and standard deviation of the number of Buddhists in a sample of 600 people from a large population where 24% of people are Buddhists.

5.      The average household income in Somerset County is $242,000 with standard deviation $74,000. If 100 households are selected at random, find the probability that their mean income will be more than $250,000.

1.)  A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.

2.)  Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

1. In words, define the random variable X.
2. List the values that X may take on.
3. Give the distribution of X. X ~ _____(_____,_____)
4. How many are expected to attend their graduation?
5. Find the probability that 17 or 18 attend.
6. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

The average number of pounds of meat that a person consumes per year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal.

a) Find the probability that a person selected at random consumes less than 224 pounds of meat per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounding to four decimal places. (4 points)

b) If a sample of 40 individuals were selected randomly, find the probability that the mean of the sample will be less than 224 pounds per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounded to four decimal places. (4 points)

c) Why are the probabilities in parts (a) and (b) so different? (2 points)

Problem 12-14 (Algorithmic)

The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $36,000. The variable cost for the product is uniformly distributed between $20 and $28 per unit. The product will sell for $56 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1,200 units and a standard deviation of 100 units. Develop an Excel worksheet simulation for this problem. Use 500 simulation trials to answer the following questions:

1. What is the mean profit for the simulation? Round your answer to the nearest dollar.
   
   Mean profit = $ ___
2. What is the probability that the project will result in a loss? Recalculate the numerical value of probability in percent and then round your answer to the nearest whole number.
   
   Probability of Loss =____ %

Suppose the incidence of ketosis in Holstein dairy cows is 11.8% in the state of Michigan (Dyk and Emery, 1996; Proc Tri-State Nutrition Conference). Assume the state of ketosis (1 = diseased, 0 = not-diseased) is independent between all animals; i.e., the occurrence or non-occurence of ketosis on any one animal is in no way related to whether ketosis occurs in any other animal. Furthermore, suppose that there are a large number of herds in the state for which the probability of ketosis (11.8%) was the same for each herd.

A)Within any one herd of size 60, what is the exact probability of having 4 or less cows being afflicted with ketosis.

B)Redo (a) but use a normal approximation to determine this probability. Do this with and without the continuity adjustment. Are either of these results consistent with the exact probability you provided in your answer to a)?

A recent survey reported that 39​% of​ 18- to​ 29-year-olds in a certain country own tablets. Using the binomial​ distribution, complete parts​ (a) through​ (e) below.

a. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, four will own a​ tablet?

The probability is ? (Type an integer or a decimal. Round to four decimal places as​ needed.)

b. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, all six will own a​ tablet?

c. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, at least four will own a​ tablet?

d. What are the mean and standard deviation of the number of​ 18- to​ 29-year-olds who will own a tablet in a survey of​ six?

e. What​ assumption(s) do you need to make in​ (a) through​ (c)?

A large car insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.

Single Policyholders Married Policyholders n1 = 450 n2 = 925 # making claim = 67 # making claim = 93

Using alpha = 0.05, determine whether the claim rates are higher for single male policyholders verses married male policyholders. Solve using the p-value approach only. Which group has the highest insurance claim percentage, single or married policyholders? Why do you think this is the case?

The following data represents number of pictures an individual has posted on Facebook (X) and their level of narcissism(Y) as measured on a 10-point scale, 10 being highest.

Analyze this data using both the correlational method as well as regression via StatsCrunch. Write the data up using APA guidelines in MS Word. Submit both your output from StatsCrunch as well as your Word document