An astronomer wants to measure the distance from his observatory to a distant star. However, due to atmospheric disturbances, any measurement will not yield the exact distance. As a result, the astronomer has decided to make n series of measurements and then use their average value as an estimate of the actual distance. If the astronomer believes that the values of the successive measurements are independent random variables that follow approximately a normal distribution with a mean of 10 light years and a standard deviation of 2 light years, how many series of measurements he needs to make so that at least 95 percent of the mean distance is less than 9.5 light years?

It takes an average of 14.5 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will increase if the patient is immediately told the truth about the injury. The EMT randomly selected 70 injured patients to immediately tell the truth about the injury and noticed that they averaged 16.3 minutes for their blood to begin clotting after their injury. Their standard deviation was 4.75 minutes. What can be concluded at the the α = 0.10 level of significance? a. For this study, we should use [Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H₁: ? Select an answer ✓ c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? ✓ a f. Based on this, we should [Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the populaton mean is significantly greater than 14.5 at a = 0.10, so…

Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°C. Assume 2.1​% of the thermometers are rejected because they have readings that are too high and another 2.1​% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

A population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ .What is the probability that the sample mean will be within +/- 5 of the population mean?

Researchers at the National Weather Center in Portland, Maine recorded the number of 90° days each year since records were first kept, starting in 1875. The number of 90° days form a normal-shaped distribution, with a mean of μ = 9.6 days and a standard deviation of σ = 1.9. To see if the data showed any evidence of climate change (and specifically global warming), they also computed the mean number of 90° days for the most recent n = 4 years and obtained a mean number of days for the past four years of x̅ = 12.25 days. Using a one-tailed test with α = .05, the researchers completed the calculations, but they need your help in drawing an appropriate conclusion. (According to their calculations, the standard error is sM = 0.95, and the sample mean of x̅ = 12.25 days corresponds to a z-score of z = 2.79.) Using the same one-tailed test (α = .05), determine if the data indicate that the past four years have had significantly more 90° days than would be expected for a random sample from…

Solve question #9 for part D only.

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 140 (borderline diabetes starts at 140)