Question

X ~ N(60, 11). Suppose that you form random samples of 25 from this distribution. Let X-bar be the random variable of averages. Let ΣX be the random variable of sums.

a. Give the distribution of X bar

(Enter an exact number as an integer, fraction, or decimal.)

b. find the probability. (Round your answer to four decimal places.)

P(X < 60) =

c. Find the 40th percentile. (Round your answer to two decimal places.)

d. find the probability. (Round your answer to four decimal places.)

P(56 < X < 62) =

e. find the probability. (Round your answer to four decimal places.)

P(24 < X < 59) =

f. Give the distribution of ΣX.

g. Find the minimum value for the upper quartile for ΣX. (Round your answer to two decimal places.)

h. find the probability. (Round your answer to four decimal places.)

P(1400 < ΣX < 1550) =

Answer 1

my dear student as per HomeworkLib rules I have solved the first 4 sub parts.