Round to 4 decimal places:

The lengths of lumber a machine cuts are normally distributed with a mean of 99 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 99.18 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 99.18 inches? (a) ne probability is D. (Round to four decimal places as needed.) About 76% of all female heart transplant patients will survive for at least 3 years. Eighty 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 69%? 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 E . I'I The probability that the sample proportion surviving for at least 3 years will be less than 69% is I]. (Round to four decimal places as needed.)