Question

Find z such that 87.7% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

Answer 1

Answer:

a) z = 1.16

b) P(x ≥ 2) = 0.8508

c) z = 1.555

Step-by-step explanation:

a) Find z such that 87.7% of the standard normal curve lies to the left of z.

Lies to the left, so it has a pvalue of 0.877. This is z = 1.16

b) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability.

μ = 2.4; σ = 0.35

P(x ≥ 2) =

This is 1 subtracted by the pvalue of Z when X = 2, in which

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2 - 2.4}{0.35}$

$Z = -1.14$

$Z = -1.14$ has a pvalue of 0.1492.

So

P(x ≥ 2) = 1 - 0.1492 = 0.8508.

c) Find z such that 6% of the standard normal curve lies to the right of z.

To the right, so z has a pvalue of 1-0.06 = 0.94%. So z = 1.555.