Sampling Probability Distributions

Please solve and show work for the following three questions:

1. A random sample of size 4 is taken from a normal population having mean 100 and variance of 25. What is the 85th percentile of the distribution of x̅?

(a) 105.18 (b) 102.59 (c) 112.96 (d) 101.30

2. A scientist anticipates that the proportion of purple blossoms in his plants is 0.18. A random sample of 52 plants indicated that 25% are purple. What is the approximate standard deviation of the sampling distribution of the sampling proportions?:

(a) 0.0600 (b) 0.0533 (c) 0.0090 (d) 0.0111

3. The average number of push-ups a U.S. Marine does daily is 300, with a standard deviation of 50. A random sample of 45 Marines is selected. What is the standard deviation of the distribution of the sample means for sample size n=45?

(a) 1.0541 (b) 2.8868 (c) 7.4536 (d) 50