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About 79% 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 74% ? 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 The probability that the sample proportion surviving for at least 3 years will be less than 74% is (Round to four decimal places as needed.)

The average math SAT score is 520 with a standard deviation of 112. A particular high school claims that its students have unusually high math SAT scores. A random sample of 40 students from this school was selected, and the mean math SAT score was 561. Is the high school justified in its claim? Explain. because the 2-score ( sample means (Round to two decimal places as needed.) since it within the range of a usual event, namely within of the mean of the