1.) On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 407 pounds and a standard deviation of 41 pounds. The cow transport truck holds 17 cows and can hold a maximum weight of 7276. If 17 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7276? (This is the same as asking what is the probability that their mean weight is over 428.)
(Give answer correct to at least three decimal places.)
probability =
2.) A population of values has a normal distribution with μ=22.5 μ=22.5 and σ=24.9σ=24.9 You intend to draw a random sample of size n=13 n=13.
Find the probability that a single randomly selected value is less than 39.1.
P(X < 39.1) =
Find the probability that a sample of size n=13 n=13 is randomly selected with a mean less than 39.1.
P(M < 39.1) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.