Assignment HW07 | Complete Solution

Assignment HW07 chapter 4 3

1. (1 point)
Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean 15 kips and standard deviation 1.55 kips. Compute the following probabilities
a. P(X < 16:95) =
b. P(17 < X < 21) =
c. P(jX 􀀀15j < 1) =
2. (1 point) 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. (1 point) Suppose x is a normally distributed random variable
with μ = 9:8 and s = 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. (1 point) 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. (1 point)
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.
Probability =
6. (1 point) 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. (1 point) 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. (1 point) Healty people have body temperatures that are normally distributed with a mean of 98:20F and a standard deviation of 0:62F .
(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99:6F? 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. (1 point) Women’s weights are normally distributed with a mean given by μ = 143 lb and a standard deviation given by s = 29 lb. Find the sixth decile, D6, which separates the bottom 60% from the top 40%.

10. (1 point) 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.