1) The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. a) For a sample of n=64, find the probability of a sample mean being less than 24.2 if =24 and =1.29= ?? (Round four decimal places as needed) b) Unusual yes or no? Why 2) Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.704 per gallon. A random sample of 35 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.683 and $2.724 that week? Assume =$0.049 a) The probability that the sample mean was between $2.683 and $2.724 is? ___(round four decimal places as needed) b) Interpret the results 3) The mean height of women in a country (ages 2029) is 63.8 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume =2.68 a) The probability mean height for the sample is greater than 64 inches is?___(Round four decimal places as needed) 4) Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 77 feet (84 inches) with a standard deviation of 0.6 inch. Assume the lengths are normally distributed. You randomly select 40 boards and find that the mean length is 84.13inches. Complete parts (a) through (c). a) Assuming the seller's claim is correct, what is the probability that the mean of the sample is84.13inches or more?____(Round to four decimal places) b) Using your answer from part (a), what do you think of the seller's claim? c) Assuming the seller's claim is true, would it be unusual to have an individual board with a length of 84.13 inches? Why or why not? 5) The average math SAT score is 518 with a standard deviation of 112 A particular high school claims that its students have unusually high math SAT scores. A random sample of 40 students from this school was selected, and the mean math SAT score was 562. Is the high school justified in its claim? Explain. a) Yes/No, because the Z score (__) is Usual/Unusual since it does not/lie within the range of a usual event namely within 1/2/3 Standard Deviations of the mean of the sample mean. (Round two decimal places) 6) bout 70% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 67%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to Squareroot of pq/n. a) the probability that the sample proportion surviving for at least 3 years will be less than 67% is? ____ (Round 4 decimal places as needed) 7) Construct the confidence interval for the population mean . c=0.95, X(bar over)=5.8, =9.0, and a) A 95% Confidence interval for is (__,__)(round to one decimal place as needed) 8) In a random sample of 35 refrigerators, the mean repair cost was $137.00and the population standard deviation is $18.30 A 90% confidence interval for the population mean repair cost is left (131.91,142.09). Change the sample size to n=70. Construct a 90% confidence interval for the population mean repair cost. Which confidence interval is wider? Explain. a) The 90% Confidence interval is? (__,__) (round two decimal places as needed) b) Which confidence interval is wider? Explain. 9). A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 33 points with 99% confidence assuming =16.5? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required? a.) A 99% confidence level requires ____ subjects. (Round to nearest Whole number) b.) How does the decrease in confidence affect the sample size required? 10) Find the critical value tc for the confidence level c=0.95 and sample size n=17. 11.) Find the margin of error for the given values of c, s, and n.c=0.98, s=66, n=21 The Margin of error is? 12.) Let p be the population proportion for the following condition. Find the point estimates for p and q. In a survey of 1032 adults from country A, 185said that they were not confident that the food they eat in country A is safe. a) The point of estimate for p, p(^ above P), is ___ (round to three decimal places as needed) b) find the point estimate for q. 13.) Use the given confidence interval to find the margin of error and the sample proportion.(0.616,0.646) A.) E= b) Find the sample proportion