3 quesitons only

1. Given that z is a standard normal random variable. Compute the following probabilities using the Cumulative Probability tables provided. Draw a normal distribution for each case and show the corresponding area for each of the following;.

a. P(-1.95 ≤ z ≤ 0.47)

b. P(0.45 ≤ z ≤ 1.15)

c. P(-.1.69 ≤ z ≤ -1.23)

d. P(z.≥ -1.6)

e. P(z ≤ 1.2)

2. Assume that the amount spent to take a driving trip for three days is $820. If the amount spent is normally distributed with a standard deviation of 240

a. What is the probability that the expenses for three days will be less than $420?

b. What is the probability that the expenses for three days will be $840 or more?

c. What is the probability that the expenses for three days will be between $500 and $1000?

d. How much are the expenses for three days for 5% of the families with the most expensive travel expenses?

3. A population has a mean of 200 and a standard deviation of 40. A sample of size 100 is selected and x̄ is used to estimate the mean, µ

a. What is the probability that the mean will be within ± 5 of the sample mean?

b. What is the probability that the mean will be within ± 10 of the sample mean?