# Question

If Z is a random variable having the standard nor–mal distribution, find the probabilities that it will take on a value

(a) Greater than 1.14;

(b) Greater than –0.36;

(c) Between –0.46 and – 0.09;

(d) Between –0.58 and 1.12.

(a) Greater than 1.14;

(b) Greater than –0.36;

(c) Between –0.46 and – 0.09;

(d) Between –0.58 and 1.12.

## Answer to relevant Questions

If Z is a random variable having the standard nor–mal distribution, find the respective values z1, z2, z3, and z4 such that (a) P(0 < Z < z1) = 0.4306; (b) P(Z ≥ z2) = 0.7704; (c) P(Z > z3) = 0.2912; (d) P(–z4 ≤ Z ...(a) Use a computer program to find the probability that a random variable having the normal distribution with mean 5.853 and the standard deviation 1.361 will assume a value greater than 8.625. (b) Interpolate in Table III ...Suppose that we want to use the normal approximation to the binomial distribution to determine b(1;150,0.05). (a) Based on the rule of thumb on page 192, would we be justified in using the approximation? (b) Make the ...If X has an exponential distribution with the parameter θ, use the distribution function technique to find the probability density of the random variable Y = lnX. If X has a uniform density with α = 0 and β = 1, show that the random variable Y = –2 ∙ lnX has a gamma distribution. What are its parameters?Post your question

0