In: Statistics and Probability
Suppose x has a distribution with μ = 10 and σ = 6.
(a) If a random sample of size n = 37 is drawn, find μx, σx and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)
μx = |
σx = |
P(10 ≤ x ≤ 12) = |
(b) If a random sample of size n = 59 is drawn, find
μx, σx
and P(10 ≤ x ≤ 12). (Round
σx to two decimal places and the
probability to four decimal places.)
μx = |
σx = |
P(10 ≤ x ≤ 12) = |
a)
Given:
= 10, = 6, n = 37
Find: P(10 < X < 12)
P(10 < X < 12) = P(0.00 < Z < 0.33)
P(10 < X < 12) = P(Z < 0.33) - P(Z < 0.00)
P(10 < X < 12) = 0.6306 - 0.5000 ...............Using standard Normal table
P(10 < X < 12) = 0.1306
b)
Given:
= 10, = 6, n = 59
Find: P(10 < X < 12)
P(10 < X < 12) = P(0.00 < Z < 0.33)
P(10 < X < 12) = P(Z < 0.33) - P(Z < 0.00)
P(10 < X < 12) = 0.6306 - 0.5000 ...............Using standard Normal table
P(10 < X < 12) = 0.1306