Problem 4. Let X be normally distributed with mean 1 and variance 2.2. (a) Find P0.5...
Exercise 2. Let consider a normally distributed random variable Z with mean 0 and variance 1. Compute (a) P(Z < 1.34). (b) P(Z > -0.01). (c) the number k such that P(Z <k) = 0.975.
X is a normally distributed variable with mean p = 30 and standard deviation o = 4. Find P(x < 40)
(10pts) 2. Assume X is normally distributed with a mean of 5 and variance of 16. Determine the value of x that solves each of the following: P(x < X < 9) = 0.2 b) P(-x < X-5<x) = 0.99
3t = 1-504 it2 for Itl < 1/71· (a) Mean ofX (b) Variance of X
Solve the problem. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If Pa <za)-0.4314,find a. 0.57 -0.18 1.49 0.3328
Assume that z-scores are normally distributed with a mean of O and a standard deviation of 1. If P(0 < z < a) = 0.4857, find a. a = (Round to two decimal places.)
6) Assume X is a normally distributed random variable with mean μ= 53 and standard deviation σ-12. Find P(52<X< 62). A) 0.5137 B)0.4269 C) 0.3066 D) 0.2108 E) 0.3635
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
SELF ASSESSMENT 1 X is a normally distributed random variable with mean 57 and standard deviation 6. Find the probability indicated P(X <59.5) а. P(X < 46.2) b. P(X> 52.2 С. d. P(X> 70) X is a normally distributed random variable with mean 500 and standard deviation 25 Find the probability indicated. а. Р(X < 400) b. P(466 < X <625) Р(X > С. Р(Х > 400)
(2.2) Let a be a real number with 1<a< 2. Put f(x) = Q +r 1+2 (a) Show that f maps (1, 0) into (1, 0). (b) Show that f is a contraction on [1, ) and find its fixed point.