Let X and Y have a bivariate normal distribution with parameters μ1 =20, μ2 = 40, σ21 = 9, σ22 = 4, and ρ = 0.6. Find the shortest interval for which 0.90is the conditional probability that Y is in the interval, given that X = 22.

A population of values has a normal distribution with μ=156.6μ=156.6 and σ=38.9σ=38.9. You intend to draw a random sample of size n=94n=94.Find the probability that a single randomly selected value is less than 147.8.P(X < 147.8) = Find the probability that a sample of size n=94n=94 is randomly selected with a mean less than 147.8.P(M < 147.8) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Assume the random variable X is normally distributed with a mean of μ=50μ=50and a standard deviation of σ=7.σ=7.Compute and find the probability  P(X>35).

Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(