1. Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean15 kips and standard deviation 1.55 kips. Compute the following probabilities
a. P(X < 16.95) =
b. P(17 < X < 21) =
c. P(|X -15| < 1) =
2. Find the following probabilities for the standard normal random variable z:
(a) P(-1.93 ≤ z ≤ 0.61) =-----
(b) P(-1.85 ≤ z ≤ 0.72) =-----
(c) P(z ≤ 1.54) =----
(d) P(z > -1.14) =-----
3. Suppose x is a normally distributed random variable with µ = 9.8 and σ = 1.6. Find each of the following probabilities:
(a) P(10.8 ≤ x ≤ 16.9) =------
(b) P(5.5 ≤ x ≤ 15) =-------
(c) P(7.4 ≤ x ≤ 16.1) =-------
(d) P(x ≥ 8.3) =
(e) P(x ≤ 13.5) =-----
4. Find the z-score such that:
(a) The area under the standard normal curve to its left is 0.5 z =----------
(b) The area under the standard normal curve to its left is 0.9826 z =-------
(c) The area under the standard normal curve to its right is 0.1423 z =--------
(d) The area under the standard normal curve to its right is 0.9394 z =--------
5. A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 6 miles. Find the probability of the following events:
A. The car travels more than 70 miles per gallon. Probability =-----
B. The car travels less than 58 miles per gallon. Probability =------
C. The car travels between 59 and 68 miles per gallon.
6. Suppose that X is normally distributed with mean 100 and standard deviation 29.
A. What is the probability that X is greater than 153.94? Probability =----
B. What value of X does only the top 17% exceed? X =--------
7. The lifetime of lightbulbs that are advertised to last for 5100 hours are normally distributed with a mean of 5400 hours and a standard deviation of 150 hours. What is the probability that a bulb lasts longer than the advertised figure?
Probability =-----
8. Healty people have body temperatures that are normally distributed with a mean of 98.20?F and a standard deviation of 0.62?F .
(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.6 ?F?
answer:------
(b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 0.5 % of healty people to exceed it?
answer:------
9. Women's weights are normally distributed with a mean given by µ = 143 lb and a standard deviation given by σ = 29 lb. Find the sixth decile, D6, which separates the bottom 60% from the top 40%.
10. The strength of an aluminum alloy is normally distributed with mean 9 gigapascals ( GPa) and standard deviation 1.41 GPa.
a. What is the probability that a specimen of this alloy will have a strength greater than 11.1 GPa?------
b. Find the first quartile of the strengths of this alloy.------
c. Find the 99th percentile of the strengths of this alloy.------