MATH221 Statistics1. Assume the random variable X is normally distributed with mean µ=85 and standard deviationơ=5. Find the indicated probability.P(X<77) = _______2. Use the normal distribution of SAT critical reading scores for which the mean is 508 and thestandard deviation is 124. Assume the variable X is normally distributed.(a) What percent of the SAT verbal scores are less than 550?Approximately _______% (round to two decimal places as needed)(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to begreater than 523? _______3. Find the z-score that has 95.8% of the distribution’s area to its right.The z-score is _______ (Round to two decimal places as needed)4. Find the z-scores for which 76% of the distribution’s area lies between –z and z.The z-scores are ______,______ (round two decimal places as needed)5. In a survey of women in a certain country (ages 20-29), the mean height was 64.9 inches with astandard deviation of 2.74 inches. Answer the following questions about the specified normaldistribution.(a) What height represents the 98th percentile? ______inches (round to two decimal places asneeded)(b) What height represents the first quartile? _______6. A population has a mean µ= 71 and a standard deviation ơ= 9. Find the mean and standarddeviation of a sampling distribution of sample means with sample size n= 81.µ¯x =_______ (simplify your answer)7. A manufacturer claims that the life span of its tires is 49,000 miles. You work for a consumerprotection agency and you are testing these tires. Assume the life spans of the tires are normallydistributed. You select 100 tires at random and test them. The mean life span is 48,772 miles.Assume ơ= 900.(a) Assuming the manufacturer’s claim is correct, what is the probability that the mean ofthe sample is 48,772 miles or less? ______( round to four decimal places as needed)8. Find the margin of error for the given values of c, s, and n.c= 0.95, s= 2.7, n= 49E=______ (Round to three decimal places)MATH221 Statistics9. Construct the confidence interval for the population mean µ.C= 0.95, ¯x= 7.9, s= 0.2, and n= 40A 95% confidence interval for µ is (______, ______). (Round to two decimal places as needed)10. Construct the confidence interval for the population mean µ.C= 0.98, ¯x= 15.5, s= 5.0, and n= 45A 98% confidence interval for µ is (______, ______). (Round to one decimal places as needed