help please, reference: https://www.studocu.com/ph/document/western-philippines-university/civil-engineering/lecture-notes/statistics-probability-q3-mod6-central-limit-theorem/12482426/view

1. A manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 120 hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is less than 900 hours? 2. The average public high school has 468 students with a standard deviation of 87. a. If a public school is selected, what is the probability that the number of students enrolled is greater than 400? b. If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is between 445 and 485? 3. In a study of the life expectancy of 400 people in a certain geographic region, the mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 68 years? 4. The number of driving miles before a certain kind of tire begins to show wear is on the average, 16800 miles with a standard deviation of 3300 miles. A car rental agency buys 36 of these tires for replacement purposes and puts each one on a different car. a. What is the probability that the 36 tires will average less than 16000 miles until they begin to show wear? b. What is the probability that the 36 tires will average more than 18000 miles until they begin to show wear? 5. Manufacturer of ball bearings claims that this product has a mean weight of 5.02 g and a standard deviation of 0.30 g. What is the probability that a random sample of 100 ball bearings will have combined weight: a. between 496 g and 500 g? b. more than 510 g