Hello,  can you help me with this math problem and show me step by step to understand this math problem. Thank you. In a random sample of 8, people the mean commute time to work was 36.5 mins and the standard deviation was 7.4 mins . A 98% confidence interval using the t-distribution was calculated (2.87, 44.3). After researching commute times to work, it was found that the population standard deviation is 8.8 mins. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. The margin of error of μ is________ (Round to two decimal places as​ needed.)

An IQ test has a mean of 100 and a standard deviation of 15. Which is more unusual, an IQ of 85 or an IQ of 120? what is the z-score for IQ 85   what is the z-score for IQ 120

A study of 96 bolts of carpet showed that their average length was 77.5 yards. The standard deviation of the population is 1.6 yards. Which of the following is the 90% confidence interval for the mean length per bolt of carpet?

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 11.25 hours with a standard deviation of 3.3 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed. (a) Find the probability that with heavy use, the battery life exceeds 12 hours. (Round your answer to four decimal places.)(b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.) hours