4 Suppose the random variable X follows a normal distribution with mean u = 54and standard...
Suppose the random variable X follows a normal distribution with mean μ=53and standard deviation σ=10. Calculate each of the following. In each case, round your response to at least 4 decimal places. a) P(X<43)= b) P(X>63)= c) P(48<X<68)=
Suppose the random variable X follows a normal distribution with mean µ = 84 and standard deviation σ = 20. Calculate each of the following: P(X > 100) P(80 < X < 144) P(124 < X < 160) P(X < 50) P(X > X*) = .0062. What is the value of X*?
QUESTION 1 A random variable X follows a normal distribution with mean 350 and standard deviation 65. If a sample of size 15 is taken, find P(X> 325). (3 decimal places)
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
Answer the question for a normal random variable x with mean u and standard deviation o specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.16. Find P(1.00<x< 1.10). P(1.00<x< 1.10) = Answer the question for a normal random variable x with mean u and standard deviation o specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.16. Find P(x >1.35). P(x > 1.35) =
Find the answer using StatCrunch. A random variable X follows a normal distribution with mean 135 and standard deviation 12. If a sample of size 10 is taken, find P (x̅ < 137). (4 decimal places)
1. X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 41, σ = 20, find P(35 ≤ X ≤ 42) 2. Find the probability that a normal variable takes on values within 0.9 standard deviations of its mean. (Round your decimal to four decimal places.) 3. Suppose X is a normal random variable with mean μ = 100 and standard deviation σ = 10....
Suppose X is a normal random variable with mean u = 50 and standard deviation o = 11. (a) Compute the z-value corresponding to X = 36. (b) Suppose the area under the standard normal curve to the left of the Z-value found in part (a) is 0.1016. What is the area under the normal curve to the left of X = 36? (c) What is the area under the normal curve to the right of X = 36? (a)...
Suppose x is a normal random variable with mean u and standard deviation o. If z is the standardized normal random variable of x, which of the following statements is false? (1) When r = y, the value of z=0. (2) When z is less than the mean y, the value of z is negative. (3) When r is greater than the mean y, the value of z is positive. (4) It is always the case that z <I.
Given a random variable X follows a Normal distribution with mean 10 and standard deviation 5, what is the probability that X lies within one standard deviation of the mean?