Suppose that 44% of all adults think that airline travel is safer than driving. An opinion poll plans to ask a simple random sample (SRS) of 1021 adults about airplane safety. The proportion of the sample who think that airline travel is safer than driving will vary if we take many samples from the same population. The sampling distribution of the sample proportion is approximately Normal with mean of 0.44 and standard deviations about 0.016. Sketch this Normal curve and use it to answer the following questions. What is the probability p that the poll gets a sample in which more than 40.8% of the people think that airline travel is safer than driving? Report your answer as a percent. p= TT P O hp 43°F Clear 6:38 PM 11/26/2022 %

A teacher wishes to give A’s to the top 8% of the students and F’s to the bottom 8%. The next 10% will be B’s and D’s, and the rest receive C’s. The scores are normally distributed with a mean of 78 and a standard deviation of 8. Use the data to find the bottom cut-off for a D grade.

A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 53% of them have an IQ score over 100 . It is known that 50% of the general population has an IQ score exceeding 100 . Find the mean of p , where p is the proportion of people with IQ scores over 100 in a random sample of 400 people. Find the standard deviation of p . Compute an approximation for P≥p0.53 , which is the probability that there will be 53% or more individuals with IQ scores over 100 in a random sample of 400 . Round your answer to four decimal places.

A notable indicator of a baby's health is the weight gained in the first year of the baby's life. Assume that the population of all such weight gains for baby girls is approximately normally distributed. A study claimed that the mean of this population is 5.28 kg. As a practicing pediatrician, you want to test this claim. So, you select a random sample of 13 baby girls, and you record the weight each gained in their first year. Follow the steps below to construct a 95% confidence interval for the population mean of all the weight gains for baby girls in their first year. Then state whether the confidence interval you construct contradicts the study's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. Number of baby girls Sample mean Sample standard deviation Take Sample 13 5.656 1.939 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need…