Stats hw please help Given 𝑍~(0,1).

Question

(a)Calculate 𝑃(𝑍 > 2.37)

(b) Calculate 𝑃(−1.28 < 𝑍 < 1.28)

(c) Find 𝑧1 given 𝑃(𝑍 < 𝑧1) = .4562

Answer 1

a)

P(z > 2.37)

standard normal distribution table lists cumulative probabilities to the left, so we could determine the above as

1 - P(z < 2.37)

or since the normal distribution is symmetric we could more easily determine the above as

P(z < -2.37) = 0.0089

b)

P(-1.28 < Z < 1.28) = P(z < 1.28) - P(Z < -1.28) = 0.8997 - 0.1003 = 0.7994

c)

Here you need to look in table for probability of 0.4562 and find z-value that corresponds to it (-1.01).