A population of values has a normal distribution with μ=27.1μ=27.1 and σ=5.6σ=5.6. You intend to draw a random sample of size n=206n=206. Find the probability that a single randomly selected value is greater than 27.9. P(X > 27.9) =  Find the probability that a sample of size n=206n=206 is randomly selected with a mean greater than 27.9. P(M > 27.9) =

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.

Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.9 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is   . The standard deviation is   . The probability that fawn will weigh exactly 2.5 kg is    P(x=2.5)=P(x=2.5)=   . The probability that a newborn fawn will be weigh between 2.6 kg and 3.7 kg is    P(2.6<x<3.7)=P(2.6<x<3.7)=   . The probability that a newborn fawn will be weigh more than 3.24 kg is    P(x>3.24)=P(x>3.24)=   . P(x>2.8∣x<3.3)=P(x>2.8∣x<3.3)=   . Find the 45th percentile.   kg

The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x. X P(x) 0 0.125 1 0.375 2 0.375 3 0.125 O A. mean: 1.50; standard deviation: 0.87 OB. mean: 1.50; standard deviation: 0.76 O C. mean: 2.25; standard deviation: 0.87 O D. mean: 2.25; standard deviation: 0.76 C