For a distribution where mean = 100 and s=20

a) find C80 (80th percentile)

b)C50

c)C20

d)median

e)What is the centile rank of the following scores

120, 80, 110

For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles.¹ The difference between these two is a measure of the depreciation on the car just by driving it off the lot. Depreciation values from our sample of 20 automobile models can be found in the dataset CarDepreciation.

Click here for the dataset associated with this question.

(a) Find the mean and standard deviation of the Depreciation amounts in CarDepreciation.

Mean =$

Standard deviation =

(b) Use StatKey or other technology to create a bootstrap distribution of the sample mean of depreciations. Describe the center and spread of this distribution.

Center =

Standard error =

(c) Use the standard error obtained in your bootstrap distribution to find a 95% confidence interval for the mean amount a new car depreciates by driving it off the lot.

The interval is $ to


¹New and used automobile costs were determined using 2015 models on kellybluebook.com.

A recent study investigated tractor skidding distances along a road in a forest. The skidding distances​ (in meters) were measured at 20 randomly selected road sites. The data are given in the accompanying table. A logger working on the road claims that the mean skidding distance is at least 425 meters. Is there sufficient evidence to refute this​ claim? Use α=0.10.

State the hypotheses to test the claim that the mean skidding distance is at least 425 meters. Choose the correct answer below.

A. H0​: μ=425

Ha​:μ ≠ 425

B. H0​: μ ≠ 425

Ha​: μ= 425

C. H0​:μ= 425

Ha​: μ < 425

D. H0​: μ = 425

Ha​: μ > 425

Calculate the value of the test statistic.

t = ________​(Round to two decimal places as​ needed.)

Calculate the​ p-value.

​p-value =_________​(Round to four decimal places as​ needed.)

Make the appropriate conclusion. Choose the correct answer below.

A. Reject H0. There is insufficient evidence at the α=0.10 level of significance to conclude that the true mean skidding distance is less than 425 meters.

B. Do not reject H0.There is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean skidding distance is less than 425 meters.

C.Do not reject H0. There is insufficient evidence at the α = 0.10 level of significance to conclude that the true mean skidding distance is less than 425 meters.

D. Reject H0. There is sufficients evidence at the α=0.10 level of significance to conclude that the true mean skidding distance is less than 425 meters.

Let X ∼Pois(µ).

(a) Find an unbiased estimator of µ. Hint: recall that E(X) = µ.

(b) What is the standard deviation of your estimator? Also recall that σ²_X = µ for Poisson r.v.’s.

Two players, A and B alternately and independently flip a coin and the first one who flip a head on top will win. Assume player A flips first. If the coin is fair, what is the probability that A wins?If A tossed N+1 times, B tossed N times, what’s the probability that A gets more heads than B?If A and B each tosses a fair coin N times. Find the probability that they get the same number of heads.

Let X be a random variable. Suppose X ∼ Exp(0.5). The area under the pdf of the Exp(0.5) distribution above the interval [0, 2] is 0.6321. What is the value of the cumulative distribution function FX of X at x = 2?

Polyester resins reinforced with fiberglass are used to fabricate wall panels of restaurants. It is theorized that adding cement kiln dust​ (CKD) to the polyester composite will increase wall panel hardness. In a​ study, hardness​ (joules [J] per squared​ centimeters) was determined for three polyester composite mixtures that used a​ 40% CKD weight ratio. The hardness values were reported as 83, 82​, and 77 J/cm^2. Research has shown that the mean hardness value of polyester composite mixtures that use a​ 20% CKD weight ratio is μ = 76 J/cm². In your​ opinion, does using a​ 40% CKD weight ratio increase the mean hardness value of polyester composite​mixtures? Support your answers statistically.

Let random variable X be uniformly distributed in interval [0, T].
a) Find the nth moment of X about the origin.
b) Let Y be independent of X and also uniformly distributed in [0, T]. Calculate the
second moment about the origin, and the variance of Z = X + Y

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99 % confidence assuming s equals 12.4 based on earlier​ studies? Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size​ required? LOADING... Click the icon to view a partial table of critical values. A​ 99% confidence level requires 64 subjects. ​(Round up to the nearest​ subject.) A 95 % confidence level requires 37 subjects. ​(Round up to the nearest​ subject.) How does the decrease in confidence affect the sample size​ required? A. The sample size is the same for all levels of confidence. B. Decreasing the confidence level increases the sample size needed. C. Decreasing the confidence level decreases the sample size needed.

Given a normal population whose mean is 680 and whose standard deviation is 48, find each of the following (use Excel to obtain more accuracy):

A. The probability that a random sample of 3 has a mean between 687 and 699.

Probability =

B. The probability that a random sample of 18 has a mean between 687 and 699.

Probability =

C. The probability that a random sample of 27 has a mean between 687 and 699.

Probability =

Use the provided excel format to formulate an answer

The Salem Board of Education wants to evaluate the efficiency of the town’s four elementary schools. The three outputs of the schools are

■   output 1 = average reading score
■   output 2 = average mathematics score

■   output 3 = average self-esteem score

The three inputs to the schools are

■   input 1 = average educational level of mothers
(defined by highest grade completed: 12 = high
school graduate; 16 = college graduate, and so on)

■   input 2 = number of parent visits to school (per child)

■   input 3 = teacher-to-student ratio

The relevant information for the four schools is given in the file P04_42.xlsx. Determine which (if any) schools are inefficient.

Use the provided excel format to explain answer

A study is planned on the physiology of exercises with human subject volunteers. The two treatments in the study are two methods of aerobic exercise training (call the methods A and B). At the end of a ten-week exercise period, each subject will undergo a treadmill test for standard respiratory and cardiovascular measurements.

Nineteen volunteers are listed in the table by sex and age. All volunteers are in good health and in the normal weight range for their age, sex, and height. Eight individuals will be tested in each the methods (A or B), so that only 16 of the 19 volunteers will be used; a subject will participate only in one of the methods.

a. Explain how you would group the individuals prior assignment of treatments so that experimental error variance could be kept at a minimum. b. Explain why you grouped as you did. c. Show your final assignment of individuals to the treatment groups.

The number of pizzas consumed per month by university students is normally distributed with a mean of 8 and a standard deviation of 4. Use Excel to answer the following questions:

A. What proportion of students consume more than 9 pizzas per month?

Probability =

B. What is the probability that in a random sample of size 9, a total of more than 81 pizzas are consumed? (Hint: What is the mean number of pizzas consumed by the sample of 9 students?)

Probability =

3. In a study of obesity the following results were obtained from samples of males and females between the ages of 20 and 75:

   n Number OverweightMales 150 21

   Females 200 48
   Can we conclude from these data that in the sampled populations there is a difference in the

   proportions who are overweight? Let a = .05.