A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3 years, and standard deviation of 2.4 years.
If you randomly purchase one item, what is the probability it will last longer than 7 years? (Give answer to 4 decimal places.)

A particular fruit's weights are normally distributed, with a mean of 645 grams and a standard deviation of 18 grams.
The heaviest 13% of fruits weigh more than how many grams?
Give your answer to the nearest gram.

Suppose that 59% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?
(Give your answer as a fraction or decimal rounded to 3 places)

About 9% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. (Remember that means should be rounded to one more decimal place than the raw data.)

3. [8 marks] Suppose a survey is conducted by Ipsos, a Canadian market research polling firm, on user satisfaction with cell phone coverage across the country. They sample 10 customers at random without replacement. Assume all sampled customers are independent. Suppose 30% of users nationwide are satisfied with their cell phone coverage.

a) [5 marks] Calculate the probability that 3 or more of the 10 randomly sampled cell phone customers are satisfied with their cell phone coverage.

b) [1 mark] Why is the probability that exactly 3 out of the 10 randomly sampled customers are satisfied with their cell phone coverage different from 0.3? Please answer in at most three sentences.

c) [1 mark] On average, in a sample of 10 customers, how many do you expect to be satisfied with their cell phone coverage?

d) [1 mark] Calculate the variance of the random variable associated with the number of satisfied customers.

On the leeward side of the island of Oahu, in the small village of Nanakuli, about 70% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, ... represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli. (a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.) P(n) = Incorrect: Your answer is incorrect. (b) Compute the probabilities that n = 1, n = 2, and n = 3. (Use 3 decimal places.) P(1) P(2) P(3) (c) Compute the probability that n ≥ 4. (Use 3 decimal places.) (d) In Waikiki, it is estimated that about 7% of the residents are of Hawaiian ancestry. Repeat parts (a), (b), and (c) for Waikiki. (Use 3 decimal places.) (a) P(n) = (b) P(1) P(2) P(3) (c)

- Determine the number of three-digit area codes that can be made from the digits 0-9, assuming the digits can repeat.

- Suppose that there are 15 people in a class. How many ways can the instructor randomly pick three students, if the order doesn’t matter?

-You are playing a game at a local carnival where you must pick a card from a normal 52-card deck. If you pick a face card (jack, queen or king) you get $2. If you pick an ace, you get $5. If you pick any other card, you have to pay $2. What is your expected value for playing this game?

-Suppose that the probability of your favorite baseball player getting a hit at each at-bat is 0.350. Assume that each at-bat is independent of any other at-bat. What is the probability that he bats five times and gets exactly two hits?

There are 50 students in a classroom at UT-Almost. Thirty of these students started as freshmen at UTA; the rest are transfers. The transfer students are split evenly between business majors and liberal arts majors. the total number of business majors is 25. (use for both questions)

#13 – If we randomly selected a single student, what is the probability he/she will be either a liberal art major or a transfer student?

ANSWER:

#16 – Suppose we randomly selected two students using this process: We take 40 envelopes and insert a slip of paper (either red or white) into each one. Each envelope is then sealed and then placed in a big box from which students draw one envelope each. The student who draw envelopes with red slips inside them are selected. Two of the envelopes contain red slips; the rest contain white. What is the probability that both students selected will be transfers?

ANSWER:

1. List all possible samples of n=2 from the following population {1,2,3,5,6,7} (note that there is no number 4 in the population). Assume that those numbers represent the years of age of six different people. Create a sampling distribution of the 15 different sample means based on each possible pair (e.g., the sample {2,1} represents on possible such pair). Assume further that the order of the numbers does not matter (e.g., the pair {1,2} is the same as the pair {2,1}). Compute the expected value of the resulting sampling distribution (i.e., the mean age or μ) based on the 15 different sample means. Compute the standard deviation (i.e., the standard error or SE) of the resulting sampling distribution based on the 15 different sample means.

2. Based on the sampling distribution you created in question 2 above, what is the probability of underestimating (i.e., the probability to the left) the true population mean age (μ) by 2 years.

Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53 pounds and a standard deviation of 3.16 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.  

b) Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.96? Give your answer to four decimal places.  

c) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 17 that weigh greater than 50 lbs? Give your answer to four decimal places.  

d) Assuming the weights of individual bags are independent, what is the probability that 8 or fewer bags weigh greater than 50 pounds in a sample of size 17? Give your answer to four decimal places.