The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 74.9 miles/hour and a standard deviation of 6.5 miles/hour.

(a) What proportion of passenger vehicles travel slower than 78 miles/hour?
(b) What proportion of passenger vehicles travel between 57 and 83 miles/hour?
(c) How fast do the fastest 10% of passenger vehicles travel? miles/hour
(d) Find a value k so that 45% of passanger vehicles travel at speeds within k miles/hour of 74.9mph. k=
(e) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5.

Please show work

The unemployment rates in the United States during

1. A ten year period is given in the following table. Use exponential smoothing to find the best forecast for next year. Use smoothing constants of 0.2, 0.4, 0.6, and 0.8. Which one had the lowest MAD?

In a survey of 1,000 adults in a country, 722 said that they had eaten fast food at least once in the past month. Create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month. Use Excel to create the confidence interval, rounding to four decimal places.

1. According to AARP, in 2008, 49% of all annual expenditure on restaurant food was by Americans age 50+. In fact AARP claims the average annual expenditure for Americans age 50+ on restaurant food in 2008 was $1960. Suppose a 2015 study randomly sampled 42 Americans age 50+ and found an average annual expenditure on restaurant food of $2145 with a standard deviation of $600. Is there reason to believe that the average annual expenditure for Americans age 50+ on restaurant food has increased since 2008 at α=.025?

   For the hypothesis stated above, what is the decision?

   	a.	Reject H0 because the test statistic is to the right of the positive critical value
   	b.	Fail to reject H0 because the test statistic is to the right of the positive critical value
   	c.	Fail to reject H0 because P-value > α
   	d.	None of the answers is correct
   	e.	Reject H0 because P-value > α

Imagine that self report measure of creativity is normally distributed with a mean of μ = 40 and a standard deviation of σ = 5

1.What is the score that cuts off the highest 10% of creative people if our sample consists of n = 100 individuals?

2.What is the score that cuts off the lowest 2% of creative people if our sample consists of 36 individuals?

Assume that females have pulse rates that are normally distributed with a mean of mu equals 76.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 70 beats per minute and 82 beats per minute. The probability is nothing. ​(Round to four decimal places as​ needed.) b. If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 70 beats per minute and 82 beats per minute. The probability is nothing. ​(Round to four decimal places as​ needed.) c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? A. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size. B. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size. C. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size. D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

The birth weights for two groups of babies were compared in a study. In one group the mothers took a zinc supplement during pregnancy. In another group, the mothers took a placebo. A sample of 129 babies in the zinc group had a mean birth weight of 3469 grams. A sample of 142 babies in the placebo group had a mean birth weight of 3318 grams. Assume that the population standard deviation for the zinc group is 843 grams, while the population standard deviation for the placebo group is 775 grams. Determine the 95% confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.

Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval.

Two Ways ANOVA

An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. She selects three feed rates and four depths of cut. She then conducts a factorial experiment and obtains the following data: (Use Minitab)

1. Analyze the data and draw conclusions. Use a = 0.05.
2. Prepare appropriate residual plots and comment on the model’s adequacy.
3. Obtain point estimates of the mean surface finish at each feed rate.

Each year, ratings are compiled concerning the performance of new cars during the firs 90 days of use. Suppose that the cars have been categorized according to whether the card needs warranty- related repair( yes or no) and the country in which the company manufacturing the car is based ( united states or not united states)Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufactured by a US – based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a US- based company is 0.025. Construct a contingency table or a Venn diagram to evaluate the probabilities of a warranty- related repair. What is the probability that a new car selected at random

a. Needs a warranty- related repair?

b. Needs a warranty repair and is manufactured by a company based in the united states?

c. Needs a warranty repair or was manufactured by a US- based company?

d. Needs a warranty repair or was no manufactured by US- based company?

Under certain​ conditions, Swiss banks pay negative

interest they

charge you.​ (You didn't think all that secrecy was​ free?) Suppose a bank​ "pays"

minus−3.93.9​%

interest compounded annually. Find the compound amount for a deposit of

​$280 comma 000280,000

after

8

years.

1. Rolling doubles When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose Elias rolls the dice 4 times. Let W = the number of times he rolls doubles. The probability distribution of W is shown here. Find the probability that Elias rolls doubles more than twice.

Data from a cloud-seeding experiment are in the file CLOUDS on the course website. The file contains rainfall in acre-feet from 52 clouds: 26 of which were chosen at random and seeded with the compound silver nitrate and the other 26 were not seeded with silver nitrate.

Simpson, Alsen, and Eden. (1975). A Bayesian analysis of a multiplicative treatment effect in weather modification. Technometrics 17, 161-166.

1. 1. Make a boxplot of the amount of rainfall from the seeded clouds. Discuss.
   2. Make a normal quantile plot of the amount of rainfall from the seeded clouds. Discuss.
   3. Find the sample mean and sample standard error of the amount of rainfall from the seeded clouds.
   4. Report a 99% confidence interval for the mean amount of rainfall from the seeded clouds.
   5. Conduct a hypothesis test of whether the true mean amount of rainfall from the seeded clouds is 750 acre-feet against the two-sided alternative that the true mean amount of rainfall from the seeded clouds is not 750 acre-feet.
2. Continuing with the data in Exercise 1, test whether cloud seeding with silver nitrate increases rainfall amounts with a 1% level of significance. Be sure to state the P-value in your report. (Sec. 7.1 and 7.2

Among drivers who have had a car crash in the last year, 130 were randomly selected and categorized by age, with the results listed in the table below. Age Under 25 25-44 45-64 Over 64 Drivers

If all ages have the same crash rate, we would expect (because of the age distribution of licensed drivers) the given categories to have 16%, 44%, 27%, 13% of the subjects, respectively. At the 0.025 significance level, test the claim that the distribution of crashes conforms to the distribution of ages

The test statistic is

χ2=

The p-value is

The conclusion is A. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

B. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

A crop scientist evaluating lettuce yields plants 20 plots, treats them with a new fertilizer, lets the lettuce grow, and then measures yield in numbers of heads per plot, with these results: 145, 142, 144, 141, 142, 155, 143, 157, 152, 143, 103, 151, 150, 148, 150, 162, 149, 158, 144, 151

The scientist is interested in testing whether the lettuce data are compatible with a population median of 150, or rather are strong evidence of a median less than 150.

Define if the following statement is true or false:

Using α =5%, the scientist can conclude that the median number of heads per plot is less than 150.

A random sample of 854 births included 431 boys. Use a 0.05 significance level to test the claim that 51.4​% of newborn babies are boys. Do the results support the belief that 51.4​% of newborn babies are​ boys?

Identify the null and alternative hypotheses for this test. Identify the test statistic for this hypothesis test.

Identify the​ P-value for this hypothesis test.

Identify the conclusion for this hypothesis test.

Do the results support the belief that 51.4​% of newborn babies are​ boys?