Given a normal distribution with μ = 50 and σ = 5, and given you select a sample of n = 100, complete parts (a) through (d).
a. What is the probability that X̄ is less than 49?
P(X̄ < 49) = 0.0228
(Type an integer or decimal rounded to four decimal places as needed.)
b. What is the probability that X̄ is between 49 and 51.5?
P(49 < X̄ < 51.5) = 0.9759
(Type an integer or decimal rounded to four decimal places as needed.)
c. What is the probability that X̄ is above 50.1?
P(X̄ > 50.1) = 0.4207
(Type an integer or decimal rounded to four decimal places as needed.)
d. There is a 40% chance that X̄ is above what value?
X̄ =
(Type an integer or decimal rounded to two decimal places as needed.)