Statistics Questions & Answers

Given degree of freedom df \( =16 \), fiad the probability by using the Student's \( t \) distribution: \( P(t>1.7)= \) Round your answer to three decimal places.

Scores for a common standardized college aptitude test are normally distributed with a mean of 518 and a standard deviation of 105 . Randomly selected students are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect. If 1 student is randomly selected, find the probability that their score is at least 588.4 . \( \mathrm{P}(X>588.4)= \) Enter your answer as a number accurate to 4 decimal places. If 5 students are randomly selected, find the probability that their mean score is at least 588.4 . \( \mathrm{P}(\bar{X}>588.4)= \) Enter your answer as a number accurate to 4 decimal places. Assume that any probability less than \( 5 \% \) is sufficient evidence to conclude that the preparation course does help students perform better on the test. If the random sample of 5 students does result in a mean score of 588.4 , is there strong evidence to support the claim that the course is actually effective? Yes. The probability indicates that it is (highly?) unlikely that by chance, a randomly selected group of students would get a mean as high as 588.4 . No. The probability indicates that it is possible by chance alone to randomly select a group of students with a mean as high as 588.4 .

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 256 feet and a standard deviation of 56 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet? \[ P \text { (fewer than } 216 \text { feet) = } \] b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled more than 228 feet? \( P \) (more than 228 feet) \( = \)

If you take a sample of size 39 , can you say what the shape of the distribution of the sample mean is? Why? If the sample size is 39 , then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30 . If the sample size is 39 , then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.

A random variable is not normally distributed, but it is mound shaped. It has a mean of 14 and a standard deviation of 5 . If you take a sample of size 13, can you say what the shape of the sampling distribution for the sample mean is? Why? If the sample size is 13 , then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30 . If the sample size is 13 , then you can say the sampling distribution of the sample mean is normally distributed since the sample size is less than 30 . If the sample size is 13 , then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30 .

(Solve these problems after the topic of Central Limit Theorem has been covered in class.)-- If a group of 40 recent college graduates is selected, what is the probability that the mean salary for this group is between 45,000 and 47,000 ?

When dragons on planet Dathomir lay eggs, the eggs are either green or yellow. The biologists have observed over the years that \( 33 \% \) of the eggs are yellow, and the rest green. Next spring, the lead scientist has permission to randomly select 60 jof the dragon eggs to incubate. Consider all the possible samples of 60 dragon eggs. What is the mean \( (\mu) \) number of yellow eggs in samples of 60 eggs? \( \mu=\square \) (Please show your answer to 1 decimal place) What is the standard deviation ( \( \sigma \) ) in the number of yellow eggs in samples of size 60 ? \( \sigma=\square \)

You may need to use the appropriate appendix table to answer this question. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. (a) What is the probability that a Dutch male is shorter than 177 cm? (Round your answer to four decimal places.) (b) What is the probability that a Dutch male is taller than 194 cm? (Round your answer to four decimal places.) (c) What is the probability that a Dutch male is between 174 and 192 cm? (Round your answer to four decimal places.) (d) out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.)

Question 7 For a standard normal distribution, use your calculator to find: \( P(z<2.33)=\square \) Round answer to at least 4 decimal places.

Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between \( z=-1.8 \) and \( z=1.8 \) standard deviations of the mean (or within 1.8 standard deviations of the mean). What percent of the data points will fall in that range? Answer: Round your percent to two decimal places and do not include the \% sign in the answer box.