Let X represent a binomial random variable with n = 380 and p = 0.78. Find the following probabilities. (Round your final answers to 4 decimal places.) Probability a. P(X ≤ 300) b. P(X > 320) c. P(305 ≤ X ≤ 325) d. P( X = 290)

A hair salon reports that on seven randomly selected weekdays, the number of customers who visited the salon were 35, 30, 28, 12, 36, 16 and 50. The population standard deviation is not given to us. Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. Interpret this. Now we have been told that we can use a normal distribution with a population standard deviation of 6. Construct a 95% confidence interval for the average number of customers who visit the salon on weekdays.

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.8 millimeters (mm) and a standard deviation of 1.7 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm


(b) the thickness is more than 7.0 mm


(c) the thickness is between 3.0 mm and 7.0 mm

Briefly explain the meaning of the statement, "critical periods represent a one-way street." How do deficits or excesses during these periods affect fetal growth and development?

In general, high school and college students are the most pathologically sleep-deprived segment of the population. Their alertness during the day is on par with that of untreated narcoleptics and those with untreated sleep apnea. Not surprisingly, teens are also 71 percent more likely to drive drowsy and/or fall asleep at the wheel compared to other age groups. (Males under the age of twenty-six are particularly at risk.)

The accompanying data set represents the number of hours 25 college students at a small college in the northeastern United States slept and is from a random sample. Enter this data into C1 of Minitab Express.

6 9 7 7 6 7 7 5 8 6 6 6 8 8 8 5 4 6 7 8 5 8 7 6 7

For the analyses that follow, we shall use

·         90%, 95%, and 99% as the confidence levels for the confidence interval.

·      5% as the level of significance ( ) for the hypothesis test.

·         7 hours sleep as the null hypothesis (according to The Sleep Foundation).

a.    List the three (3) assumptions for a valid confidence interval and hypothesis test. Provide an explanation as to whether or not each one is met - more than just a simple “yes” or “no” – and refer to the boxplot and normal probability plot, as necessary, in your assessment.

b.    What degrees of freedom will you use for the t distribution? Show your calculation.

(Hint: degrees of freedom is n-1.)

TRUE OR FALSE

1. A t-test is used when the population standard deviation is known.

2. The degrees of freedom in a t-test is one less than the margin of error.

3. A confidence interval can only be found when the standard deviation of the population is known.

4. The margin of error for a t-test is calculated using the sample mean.

5. The null hypothesis is a claim made about the sample.

6. The significance level is denoted by n.

7. If the conclusion of a hypothesis test is “fail to reject the null hypothesis,” then the results are statistically significant.

8. A 95% confidence interval for a population mean must be calculated using the sample mean.

9. A z-score is a test statistic.

10. A t-statistic is the same for a 95% confidence interval and a 90% confidence interval regardless to the same size.

In a large hospital, a nursing director selected a random sample of 30 registered nurses and found that the mean of their ages was 30.2. The population standard deviation for the ages is 5.6. She selected a random sample of 40 nursing assistants and found the mean of their ages was 31.7. The population standard deviation of the ages for the assistants is 4.3. Find the 99% confidence interval of the differences in the ages.

Please provide an aswer and reference(s) to the question below from a classmate. Thank you in advance!

Class,

I am having a problem with the following problem:

A certain brand of automobile tire has a mean life span of 39,000 miles and a standard deviation of 2,250 miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.)

For the life span of 34,000 miles, z-score is = 34,000 x 39,000 = -2.22

2,250

For the life span of 34,000 miles, z-score is = 38,000 x 39,000 = -0.44

2,250

For the life span of 34,000 miles, z-score is = 31,000 x 39,000 = -3.56

2,250

The following is the part I am having trouble with:

The life spans of three randomly selected tires are 34,500 miles, 43,500 miles, and 39,000

miles. Using the empirical​ rule, find the percentile that corresponds to each life span:

1. The life span 34,500 miles corresponds to the ___th percentile?

2. The life span 43,500 miles corresponds to the ___th percentile?

3. The life span 39,000 miles corresponds to the ___th percentile?

I have found in the text in Chapter 2, p.88 where it talks about Empirical Rules and Bell-Shaped Distribution. I did find that number 3 is "50"th percentile, as it is also the mean value in this problem set. Numbers 1 and 2 I am having an issue calculating. Any help from my battle buddies would be outstanding. Thank you in advance!

Reference:

Larson, R. & Farber, B. (2015). Elementary Statistics: picturing the world. 6th edition.

The mean per capita consumption of milk per year is 133 liters with a variance of 576.

If a sample of 195 people is randomly selected, what is the probability that the sample mean would differ from the true mean by less than  3.62  liters? Round your answer to four decimal places.

Begin this discussion by first stating your intended future career. Then give an example of a mean that applies to two Populations for which you would like to do a Hypothesis Test in your future career. In your Hypothesis Test you will be testing the difference between these two Population means when the two samples are independent. Your discussion MUST include the two target Populations along with the Population characteristic that your mean is computed for, and the unit that is used when taking the sample measurements. As shown in the text your Null and Alternative Hypotheses MUST include a symbol for each of the two Population means along with the relational operator that describes the difference being tested between these two parameters as stated in your discussion.

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 600 and a standard deviation of 90. (a) Find the credit score that defines the upper 5 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score (b) Seventy-five percent of the customers will have a credit score higher than what value? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) Credit score (c) Within what range would the middle 80 percent of credit scores lie? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) Range-- to---

Complete the following problems using R.  Name the file with your last name, e.g., “Prob set 6-Smith.eoc”Clearly label problems, and be sure to turn in explanations and interpretations where appropriate.

3.Total cholesterol has been reported to be 200 mg/dL on average in the US by the Centers for Disease Control.  You measure total cholesterol on a random sample of 80 Alabama adults, with the intention of comparing Alabamians’ cholesterol level to that of the US average. Data are included in the assignment .xlsx file. Assume

that cholesterol is approximately normally distributed with a known standard deviation of 70 mg/dL.

a.What is the mean value observed for Alabamians’ cholesterol?

b.What is the standard error of Alabamians’ cholesterol assuming the given known standard deviation?

c.Find the 95% confidence interval for the unknown population mean of Alabamians’ cholesterol level values and interpret its meaning.

d.Test the hypothesis that Alabamians have higher average cholesterol than that of the US at the =0.05 level.  (Be sure to right down all steps, as in the lecture notes, and interpret the meaning of the test!)

e.How would your answer in (d) change if you used an =0.01 level?

A recent college graduate is planning to take the first three actuarial certification exams over the course of the next year, the first one in June, second in July and third in August. If she fails any, she will not take the remaining exams. The probability she passes the first is 0.9. Given that she passes the first exam, she has a 0.75 chance of passing the second and given that she passes both the first and second, she has a 0.65 chance of passing the third. (a) What is the probability she passes all three exams? (b) Given that she did not pass all three exams, what is the probability that she failed the second? (c) Given that she did not pass all three exams, what is the probability that she failed the third?