. Heights of fences are normally distributed with a mean of 54 inches and a standard deviation of 5 inches. Find the probability that one randomly selected fence is under 58 inches. (Answer must be given to fourdecimal places.)

2. A sample of 80 retirees is drawn at random from a normal population whose mean age and standard deviation are 70 and 8 years, respectively. Find the standard error of the sampling distribution of the sample mean. (Answer must be given to four decimal places.)

3. Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the probability P(X = 75) using the normal distribution (round your answer to 2 decimal places.)

4. A sample of size 36 is taken from an infinite population whose mean and standard deviation are 49 and 10, respectively. The probability that the sample mean is larger than 52 equals: