# Point Estimate of Statistics and Probability Calculation

1. A simple random sample of five months of sales data provided the following information

Month 1 2 3 4 5

Units Sold 94 100 85 94 92

a. Develop a point estimate of the population mean number of units sold per month.

b. Develop a point estimate of the population standard deviation

2. The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):

Critical Reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is o = 100.

a. What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

b. What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)?

c. What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test (to 4 decimals)?

© BrainMass Inc. brainmass.com October 17, 2018, 11:25 am ad1c9bdddfhttps://brainmass.com/statistics/hypothesis-testing/point-estimate-of-statistics-and-probability-calculation-538508

#### Solution Preview

1. a. The point estimate is the sample mean. The sample mean is (94+100+85+94+92)/5=93

b. The point estimate is the sample standard deviation. The sample standard deviation is sqrt{[(94-93)^2 + (100-93)^2 + (85-93)^2 + (94-93)^2 + (92-93)^2]/(5-1)}=5.385

2. a. What is the probability a random sample of 90 test ...

#### Solution Summary

The solution gives detailed steps to calculation the point estimate of population mean and standard deviation. Also, the probabilities in a sample with known sample mean and standard deviation are computed step by step.

Five reasons for sampling; use of descriptive statistics; verbal SAT score for athletes

Please see attached files.

Please Include:

The page number from the attached pdf (Chapter 8) where the appropriate formula or guidance is located on how to solve the problem.

The steps involved in reaching the solution.

The solution.

1 The Lind text lists 5 reasons for sampling. List them and give an example of each type.

2 Using the descriptive statistics data determined during Week One's weekly problem discussion, the mean for EI followed a standard distribution with a mean of 132.83 and a standard deviation of 15.68. If we selected another random sample of 50 participants, Note for #2: All the information you need to solve the question is contained in the question.

a What is the likelihood of selecting a sample with a mean EI score of at least 134?

b What is the likelihood of selecting a sample with a mean EI score of more than 128?

c What is the likelihood of selecting a sample with a mean EI score of more than 128 but less than 134?

Please show likelihood as a decimal with two decimal places.

3 The mean Verbal SAT score for Division I student-athletes is 523 with a standard deviation of 103. If you select a random sample of 60 of these students, what is the probability the mean is below 300? Above 450?