1. The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces. a. What is the probability that a shoe weighs more than 13 ounces? b. What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?2. A study of 800 homeowners in a certain area showed that the average value of the homes was $82,000, and the standard deviation was $5000. If 50 homes are for sale, find the probability that the mean of the values of these homes is greater than $83,500.3. A random sample of 20 acres gave a mean yield of sugarcane equal to 41.2 tons per acre with a standard deviation of 3 tons. Assuming that the yield of sugarcane per acre is normally distributed, a. Construct a 90% confidence interval for the population mean. b. What is the margin of error for this estimate in part a?4. A federal report indicated that BTW: of children ages 2 to 5 years had a good dietan increase over previous years. How large a sample is needed to estimate the true proportion of children with good diets within 2% with 95% confidence\";I