a) Let z be a random variable with a standard normal distribution. Find the indi

Question

a) Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(0 z 1.63)

b)Consider a normal distribution with mean 33 and standard deviation 10. What is the probability a value selected at random from this distribution is greater than 33? (Round your answer to two decimal places.)

c)Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

= 38; = 14

P(50 x 70) =

d)Find z such that 7.1% of the standard normal curve lies to the left of z

Explanation / Answer

P(X < A) = P(Z < (A - )/)

a) P(0 z 1.63) = P(z 1.63) - P(z 0)

= 0.9484 - 0.5

= 0.5484

b) P(X > 33) = 0.5

c) P(50 x 70) = P( x 70) - P(x 50)

= P(Z < (70-38)/14) - P(Z < (50-38)/14)

= P(Z < 2.29) - P(Z < 0.86)

= 0.9890 - 0.8051

= 0.1839

d) P(Z < X) = 0.071

From standard normal distribution table, z = -1.47

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