***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

7) For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

a. What is the probability that the debt for a borrower with good credit is more than $18,000?

b. What is the probability that the debt for a borrower with good credit is less than $10,000?

c. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?

d. What is the probability that the debt for a borrower with good credit is no more than $14,000?

According to a 2009 Reader's Digest article, people throw away about 9% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 122 grocery shoppers to investigate their behavior. What is the probability that the sample proportion does not exceed 0.10?

Standard Deviation of Sample Proportion:     

Answer format: .####

z score:      Answer format: .####

Probability:     Answer format: .####

Note: You should keep standard deviation of phat #, z score and probability to 4 decimal places in your calculations.

Use TI 84 to get the probability.

8. Adam, Bonnie, Chuck, Dave and Elaine are engineers from different companies attending a professional conference at the University of Arizona in Tucson. There are seven hotels near the campus. Each engineer will stay at a randomly picked hotel. a. What is the probability that they will all stay at the same hotel? b. What is the probability that they will all stay at different hotels? c. Adam has a crush on Bonnie, what is the probability that they will stay at the same hotel? d. What is the probability that exactly two of the five engineers will stay at the same hotel with no one else staying at a same hotel?

An insurance company believes that people can be divided into two classes: those who are accident-prone and those who are not. Their statistics show that an accident-prone person will have an accident at some time within a fixed one-year period with probability 0.4, whereas this probability decreases to 0.2 for a non-accident-pron person Assume that 30% of the population is accident-prone.

a) What is the probability that a new policyholder will have an accident within a year of purchasing a policy?

b) Suppose that a new policyholder has an accident within a year of purchasing a policy What is the probability that he or she is accident-prone?

c) What is the conditional probability that a new policyholder will have an accident in his or her second year of policy ownership, given that the policyholder had an accident in the first year?

The age distribution for the employees of a highly successful “start-up” company head-quarted in Jakarta is shown in the following data. Age 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Proportion 0.02 0.04 0.05 0.07 0.04 0.02 0.07 0.02 0.11 0.07 0.09 0.13 0.15 0.12 An employee is to be randomly selected from this population.

a. Can the relative frequency distribution in the table be interpreted as a probability distribution? Explain.

b. Graph the probability distribution.

c. What is the probability that the randomly selected employee is under 30 years old?

d. What is the probability that the randomly selected employee is over 40 years old?

e. What is the probability that the randomly selected employee will be between 25 to 30 years old?

1. We are interested in analyzing data related to football players for one season. Use T to denote the player is in their 30s and use F to denote a player plays offense. The probability that someone in their 30s in the data set is 10.2%. The probability that someone plays offense in the data set is 48.6%. The probability that someone is in their 30s and plays offense if 4.9%.
   1. What percentage of people in the NFL are in their 30s or play offense?
   2. What percentage of people in the NFL are in their 30s and do NOT play offense?
   3. Given someone is in their 30s, what is the probability that they play offense?
   4. What percentage of players are NOT in their 30s and are NOT on offense?
   5. Are T and F mutually exclusive events? Why or why not?
   6. Are T and F independent events? Explain, using probabilities.
   7. If we know someone plays offense, what is the probability they are in their 30s?

Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.80 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions.

(a) What is the probability that a single detection system will detect an attack?

(b) If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

(c) If three systems are installed, what is the probability that at least one of the systems will detect the attack?

(d) Would you recommend that multiple detection systems be used? Explain.

Multiple detection systems (should or should not) be used because P(at least 1) for multiple systems (is or is not) very close to 1.

Put formulas and answers in yellow shaded cells.

1) The probability of having black hair.

2) The probability of having blonde hair.

3) The probability of being male and having brunette hair.

4) The probability of having red or black hair.

5) The probability of being male or having brunette hair.

Suppose a professor of probability is tired of reading the depressing news and so he decides that he will quickly scan the first 5 headlines in the New Yorks Times and the first 5 headlines in the Boston Globe and if at most 3 of the articles in each are depressing, he will read the news that day. Further suppose that the probability of a NYTs headline being depressing is 0.6 and for the Globe the probability of a headline being depressing is 0.55.

(a) What is the probability that he will read the news the first day he tries this?

(b) In order to be "well-informed" he needs to read the news at least half the time; what is the probability that he will be well-informed after doing this for a week?

Hint: This is another problem where there are two independent parts of the random experiment. You might want to phrase it as three different random variables, all three binomial.

The weights of chocolate chip cookies are normally distributed (bell-shaped) with an average weight of 12 ounces and a standard deviation of 0.25 ounces

1) If a bag of chocolate chip cookies is chosen at random, what is the probability that it will weigh more than 12 ounces?

2) If a bag of chocolate chip cookies is chosen at random, what is the probability it will weight between 11.5 and 12.5 ounces?

3)If a bag of chocolate chip cookies is chosen at random, what is the probability that it will weigh more than 11.75 ounces?

4) If a bag of chocolate chip cookies is chosen at random, what is the probability it will weight between 11.25 and 12.75 ounces?

5) If a bag of chocolate chip cookies is chosen at random, what is the probability that it will weigh more than 12.5 ounces but less than 12.75 ounces?