Given that ?~?(15,1.252 ), find: a. ?(? ≤ 15) b. ?(? > 10) c. ?(|? − 15| < 3) d. Find the 95th percentile of X
Solution :
Given that ,
mean =
= 15
standard deviation =
= 1.25
(a)
P(x
15) = P((x -
) /
(15 - 15) / 1.25) = P(z
0)
Using standard normal table,
P(x
15) = 0.5
(b)
P(x > 10) = 1 - P(x < 10)
= 1 - P((x -
) /
< (10 - 15) / 1.25)
= 1 - P(z < -4)
= 1 - 0
= 1
P(x > 10) = 1
(c) P(|X - 15| < 3) = P(|X - 15 / 1.25| < 3 - 15 / 1.25)
= P(|z| < -9.6)
= 2 * P(Z < -9.6)
= 2 * 0
P(|X - 15| < 3) = 0
(d)
P(Z < z) = 95%
P(Z < 1.645) = 0.95
z = 1.645
5Using z-score formula,
x = z * +
x = 1.645 * 1.25 + 15 = 17.05625
95th percentile = 17.06
Get Answers For Free
Most questions answered within 1 hours.