Answer to Question #325550 in Statistics and Probability for Lala

Question

What's More

Let's see how well you understood our discussion. At this point, I want you to

solve the following problems. Show your complete solution by following the step-by-

step procedure.

1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand

of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is

normally distributed.

a. If a cup of ice cream is selected, what is the probability that the cholesterol

content will be more than 670 mg?

b. If a sample of 10 cups of ice cream is selected, what is the probability that

the mean of the sample will be larger than 670 mg?

2. In a study of the life expectancy of 400 people in a certain geographic region, the

mean age at death was 70 years, and the standard deviation was 5.1 years. If a

sample of 50 people from this region is selected, what is the probability that the

mean life expectancy will be less than 68 years?

Answer 1

1.

a. $(X>670)=1−P(X≤670) =1-P(Z\leq\dfrac{670-660}{35})=1−P(Z≤ \frac{ 670−660}{35} ​ ) \approx1-P(Z\leq0.2857)=1-0.61409=0.38591$

b.$(X>670)=1−P(X≤670) =1-P(Z\leq\dfrac{670-660}{35/\sqrt{10}})=1−P(Z≤ \frac{ 670−660}{35/\sqrt{10}} ​ ) \approx1-P(Z\leq0.9035)\approx0.1831$

2.

$P(X<68)=P(Z<\frac{68-70}{5.1/\sqrt{50}})=P(Z<-2.77)=0.0028$