Question

1) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 120.4-cm and a standard deviation of 1.4-cm.
Find the probability that the length of a randomly selected steel rod is less than 120.1-cm.
P(X < 120.1-cm) =

2) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 236.7-cm and a standard deviation of 2.4-cm. For shipment, 10 steel rods are bundled together.
Find P₁₈, which is the average length separating the smallest 18% bundles from the largest 82% bundles.
P₁₈ =

3) A population of values has a normal distribution with μ=132.5μ=132.5 and σ=20.6σ=20.6. You intend to draw a random sample of size n=119n=119.
Find P₃₈, which is the mean separating the bottom 38% means from the top 62% means.
P₃₈ (for sample means) =

4) A population of values has a normal distribution with μ=109.1μ=109.1 and σ=34.1σ=34.1. You intend to draw a random sample of size n=208n=208.
Find P₇, which is the score separating the bottom 7% scores from the top 93% scores.
P₇ (for single values) =
Find P₇, which is the mean separating the bottom 7% means from the top 93% means.
P₇ (for sample means) =

5) CNNBC recently reported that the mean annual cost of auto insurance is 961 dollars. Assume the standard deviation is 294 dollars. You take a simple random sample of 67 auto insurance policies.
Find the probability that a single randomly selected value is at least 975 dollars.
P(X > 975) =
Find the probability that a sample of size n=67n=67 is randomly selected with a mean that is at least 975 dollars.
P(M > 975) =

Answer 1