Respuesta :
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2 - 2.4}{0.35}[/tex]
[tex]Z = -1.14[/tex]
[tex]Z = -1.14[/tex] 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.
