The probability that a certain kind of flower seed will germinate is .80.

(a) If 194 seeds are planted, what is the probability that fewer than 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability()

(b) What is the probability that at least 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability ()

For the past 104 ​years, a certain state suffered 27 direct hits from major​ (category 3 to​ 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts​ (a) through​ (d). a) What is the probability that the state will not be hit by any major hurricanes in a single​ year? The probability is nothing.​ (Round to four decimal places as​ needed.) ​(b) What is the probability that the state will be hit by at least one major hurricane in a single​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Is this​ unusual? Yes No ​(c) What is the probability that the state will be hit by at least three major hurricanes in a single​ year, as happened last​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Does this indicate that the 2004 hurricane season in this state was​ unusual?

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Compute the probability of receiving four calls in a 5-minute interval of time.

b. Compute the probability of receiving exactly 9 calls in 15 minutes.

c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?

d. Suppose, no calls are currently on hold, If the agent takes 5 minutes to complete the current call, what is the probability that no callers will be waiting?

e. If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

A ski gondola carries passengers to the top of a mountain. A plaque states that its maximum capacity is 12 people or 2019 lbs. Men’s weights are normally distributed with a mean of 179 lbs and a standard deviation of 30 lbs.

a)

What is the probability that 12 randomly-selected men will exceed the weight limit of the gondola?

b)

Suppose you are the engineer in charge of safety at the mountain. What is the maximum number of men you would allow to ride the gondola at a time in order to be confident they would not exceed the weight limit? Explain.

c)

Suppose the gondola carries the maximum number of men (as given in part b) on every trip. The gondola operates for eight hours a day, and each trip takes 15 minutes to complete. What is the expected amount of time before you lose your licence? Does this answer lead you to rethink your answer to part b)? If so, what would you do differently in part b) (you don’t have to redo part b)?

Indicate using either a “B” (binomial) or a “P” (Poisson) which distribution you would use to predict random frequencies in the following data:

Number of teeth per person with cavities in the population
Number of times a fish inhales within a given time period
Number of Girl Scout cookie boxes sold in front of Walmart each day
Number of Drosophila legs with fewer than 5 bristles
Number of mitochondria in a cell

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 42% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.) (a) half or more of the claims have been padded (b) fewer than 45 of the claims have been padded (c) from 40 to 64 of the claims have been padded (d) more than 80 of the claims have not been padded

3.27. Problem. (Section 11.5) The following are applications of Theorem 11.6 or the Central Limit Theorem.

(a) Determine the distribution of (1/5)X₁ + (2 /5)X₂ + (2/5)X₃ if X₁, X₂ and X₃ are independent normal distributions with µ = 2 and

σ = 3.

(b) The weight (kg) of a StarBrite watermelon harvested under certain environmental conditions is normally distributed with a mean of 8.0 with standard deviation of 1.9. Suppose 24 StarBrite watermelons grown in these conditions are harvested; compute the probability that the average weight of all 24 watermelons is less than 7.8 kg/fruit

(c) A study of elementary school students reports that the mean age at which children begin reading is 5.7 years with a standard deviation of 1.1 years. If 55 elementary school students are selected at random, approximate the probability that the average age at which these 55 children begin reading is at least 6.

(d) Let the random variable X be defined as the number of pips that show up when a fair, six-sided die is rolled. The mean and standard deviation of X can be shown to be µX = 3.5 and σX = 1.71, respectively. If 100 fair, six-sided dice are rolled, aproximate the probability that the mean of number of pips on the 100 dice is less than 3.25

What is the best statistical analysis to use when determining if verbal reinforcement affects response rates?

Come up with a research example (not in the text) of when it would be appropriate to use a repeated-measures design. Describe the study. Come up with a research example (not in the text) of when it would be appropriate to use a matched-pairs design. Describe the study. Come up with a research example (not in the text) of when it would be appropriate to use a pretest/posttest design. Describe the study. Imagine that you needed 10 pairs of scores in your matched-pairs study. How many different individuals would you need? Imagine that you needed 10 pairs of scores in your repeated-measures study. How many different individuals would you need? What is one of the benefits of choosing a related-samples design?

(2) Suppose the original regression is given by y = β0 + β1x1 + β2x2 + β3x3 + u. You want to test for heteroscedasticity using F test. What auxiliary regression should you run? What is the

null hypothesis you need to test?

A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for μ is . Part 2 of 2 (b) If the sample size were =n89, would the margin of error be larger or smaller? ▼(Choose one) , because the sample size is ▼(Choose one).

In a poll, 412 of 1030 randomly selected adults aged 18 or older stated that they believe there is too little spending on national defense. Use this information to complete parts (a) through (d) below.

(A) Obtain a point estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense.

(B) Are the requirements for construction a confidence interval about p satisfied?

-a) Yes, the requirements are satisfied.

-b) No, the requirements of the sample being a random sample are not satisfied.

-c) No, the requirement that np(1-p) is greater than 10 is not satisfied.

-d) No, the requirement that the sample size is no more than 5% of the population is not satisfied.

C) Construct a 90% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national defense.

The 90% confidence interval is ( ___ , ___ )

D) Is it possible that more than 45% of adults aged 18 or older believe there is too little spending on national defense? Is it likely?

-a) It is possible, but not likely.

-b) It is not possible.

-c) It is possible and likely.

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4

(a) Use a calculator with mean and standard deviation keys to find x bar and s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.) x bar = x bar = % s = %

(b) Compute a 90% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %

(c) Compute a 99% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %

(d) The home run percentages for three professional players are below. Player A, 2.5 Player B, 2.2 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

We can say Player A falls close to the average, Player B is above average, and Player C is below average.

We can say Player A falls close to the average, Player B is below average, and Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is below average.

(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.

No. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.