A) According to the National Institute of Health, 34% of adults in the United States are overweight. Suppose we sample 20 adults. Let X denote the number of overweight people among them.

What is the probability that more than 6 of the adults will be overweight? Round to four decimal places.

B) According to the National Institute of Health, 34% of adults in the United States are overweight. Suppose we sample 20 adults. Let X denote the number of overweight people among them.

What is the probability that exactly 5 of the adults will be overweight? Round to four decimal places.

C) The weight of infants at a New York hospital has a mean of 7.5 pounds and a standard deviation of 0.95 pounds. Weights are approximately normally distributed.

What is the probability that a randomly selected infant will have a weight between 6.8 pounds and 7.9 pounds? Round to four decimal places.

D) The lengths of pregnancies are normally distributed with a mean of 248 days and a standard deviation of 15 days. If a pregnant woman is randomly selected, what is the probability that her pregnancy lasts more than 275 days? Round to four decimal places.

               Are you approximately normal?     

1. A study found that only 60% of all married women say that they would marry the same man “if they could do it all over again”. If we randomly sample 15 married women, find the probability that –

1. exactly twelve say they would marry the same man “if they could do it all over again”.

2. at least twelve say that they would marry the same man “if they could do it all over again”.

3. fewer than twelve say that they would marry the same man “if they could do it all over again”.

4. In a sample of 200 married women, would it be unusual to find 130 who say they would marry the same man “if they could do it all over again? Justify your answer.

#32

Is there a relation between police protection and fire protection? A random sample of large population areas gave the following information about the number of local police and the number of local fire-fighters (units in thousands). (Reference: Statistical Abstract of the United States.)

Use a 5% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of number of police and number of firefighters.

(a) Rank-order police using 1 as the largest data value. Also rank-order firefighters using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.

(c) Compute the sample test statistic. (Use 3 decimal places.)

1. Below is the probability distribution for X which represents the number of cutthroat trout caught in a six-hour period at Pyramid Lake, Nevada.

                     x      0      1      2      3       4   .

                 p(x)   .44    .36            .04     .01     

1. Find the missing probability.

2. Find the expected number of cutthroat trout caught in a six-hour period at Pyramid Lake, Nevada.

3. Find the standard deviation of X.

4. Find the probability of catching at least 3 cutthroat trout in a six-hour period at Pyramid Lake, Nevada.

BINOMIAL PROBABILITIES Big Box Store (BBS) has an annual rate of 4% of all sales being returned. In a recent sample of thirty randomly selected sales the number of returns was five. BBS is concerned about the event, and your advice is solicited. ( FOR 4 – 9, OPEN THE EXCEL EXAM TWO FILE. THE SPREADSHEET FOR THIS PROBLEM IS FOUND ON SHEET TWO. COMPLETE AND SAVE YOUR WORK IN EXCEL AND ENTER THE SOLUTIONS BELOW. (6) (2.5points) What is the probability that a random sample of 30 sales has 5 or fewer returns? Type the answer and any work below.   (7) (2.5 points) What is the probability that a random sample of 30 sales has less than four returns? Type the answer and any work below.

In 2018, as a way of commemorating the 10-year anniversary of the release of the first smartphone, an undergraduate student polled a random sample of 26 her peers in hopes of estimating the average time (in hours) such students spend on their smartphone each day, on average. Using the data she collected, she produced a 95% confidence interval for the true mean time college students spend on their phone each day: (5.035, 6.165)

1. What was the margin of error of this confidence interval?

2. What was the sample mean time (in hours) for the n = 26 students?

3. What was the sample standard deviation (in hours) for the n = 26 students? Submit your answer rounded to four decimals.

Show work please and thank you.

BINOMIAL PROBABILITIES Big Box Store (BBS) has an annual rate of 4% of all sales being returned. In a recent sample of thirty randomly selected sales the number of returns was five. BBS is concerned about the event, and your advice is solicited. FOR 4 – 9, OPEN THE EXCEL EXAM TWO FILE. THE SPREADSHEET FOR THIS PROBLEM IS FOUND ON SHEET TWO. COMPLETE AND SAVE YOUR WORK IN EXCEL AND ENTER THE SOLUTIONS BELOW. (6) (2.5points) What is the probability that a random sample of 30 sales has 5 or fewer returns? Type the answer and any work below.  

The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5.

Find the Z-score of a 50 year old employee.

What is the probability that a randomly chosen employee will be younger than 35 years?

What is the probability that a randomly chosen employee will have an age between 35 and 45 years?

What is the probability that a randomly chosen employee will be older than 55 years?

Find the Z-score of a 35 year old employee.

A population has a mean of 50 and a standard deviation of 5. A sample of 100 observations will be taken. The probability that the mean from that sample will be between 49 and 51 is

a)0.50

b)0.6826

c)0.8413

d)0.9544

n1=37, n2=37, s1= 7.4345, s2= 3.4927, x1= 23.237, x2 = 22.526 Please perform: One Hypothesis test, an F test for the equality of the variances of travel Times and the second test is a T-test for the equality of the means of travel times in MINUTES. The F test must be performed first in order to select either Case1 or Case 2 for the T-test. Then perform the Required T-test (either case 1 or 2 depending on your findings of the F-test). use p value as rejection rule for both tests!!, and use the 5 steps please please help

-the pvalue has to be used as rejection rule, and an f test then a t test (case 1 or 2 depending on f test results). The answers have to be in an interval. Please help me. I need this to review and study. I dont know how to get them in an interval. please make sure the p value is used

Consider a case-control study of the possible association between alcohol consumption and the risk of esophageal cancer as reported by Tyns et al. (1977). The study entailed 200 males diagnosed with esophageal cancer in one of the regional hospitals between the years1972 and 1974, and controls were a sample of 775 adult males selected from electoral lists in each community. The data on alcohol consumption dichotomized at a value of 80 g/d for cases and controls are summarized below:

Average alcohol consumption (g)                  Cases   Controls          Total

>80                                                      96        109                  205

<80                                                      104      666                  770

Total                                                    200      775                  975

Carry out a test of possible association between the average daily alcohol consumption and the risk of esophageal cancer. Calculate 95% CIs of the measure of association and interpret your findings.

#33 Babita

Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/l. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements are shown below. (Reference: EPA Wetland Case Studies.)

Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings.

(a) Rank-order the inlet readings using 1 as the largest data value. Also rank-order the outlet readings using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.

(c) Compute the sample test statistic. (Use 3 decimal places.)

what is a bootstrap in statistics? How do we get p-values and confidence intervals using bootstrapping?

The profit function for two products is:

    Profit = −3x ₁² + 42x ₁ − 3x ₂² + 48x ₂ + 700,

where x ₁ represents units of production of product 1, and x ₂ represents units of production of product 2. Producing one unit of product 1 requires 5 labor-hours, and producing one unit of product 2 requires 6 labor-hours. Currently, 24 labor-hours are available. The cost of labor-hours is already factored into the profit function, but it is possible to schedule overtime at a premium of $5 per hour.

Formulate an optimization problem that can be used to find the optimal production quantity of products 1 and 2 and the optimal number of overtime hours to schedule.

Solve the optimization model you formulated. How much should be produced and how many overtime hours should be scheduled? If needed, round your answers to two decimal digits.

Write a short essay on scientific writing and explain its different components?