Part I1(Form A) Elementary Statistics partmental Final Exam Problem #2 (12 point

Question

Part I1(Form A) Elementary Statistics partmental Final Exam Problem #2 (12 points) An aut city under normally distribut a new model that averages 27 miles per gallon in th omobile manufacturer introduces ormal conditions. Assume that in-city mileage for this ed with standard deviation of 2.5 miles per sallon. a. What is the probability that a person who will purchas (5 points) cr hat averages between 25 and 29 miles per gallon for in-city driving b. Find the value of the 90th percentile, Pso, for this random variable. (5 points) Use information from part (b) to circle the correct choice and to fill in the blanks in the following sentence: c. 2 points) % of the new model cars average (at least/at most) in-city driving miles per gallon for Show your work. Partial credit will be given

Explanation / Answer

Let's write the given iinformation.

X follows normal distribution with mean = 27 miles and standard deviation = 2.5 miles.

a) We want to find P(25 < X < 29) = P(X < 29) - P(X < 25) .....(1)

Let's used excel to find normal probabilities:

the general command to find normal probability in excel is "=NORMDIST(x, mean, standard deviation, 1)"

P(X < 29) = =NORMDIST(29,27,2.5,1) = 0.788145

P(X < 25) = =NORMDIST(25,27,2.5,1) = 0.211855

Put these values in equation 1), we get

P(25 < X < 29) = 0.788145 - 0.211855 = 0.576289

b) We want tpo find 90th percentile such that.

P(X < x) = 0.90

The general command to find x for the given probability is "=NORMINV(probability, mean, standard deviation)"

therefore x = "=NORMINV(0.9,27,2.5)" = 30.20388

c) (90)%  of the new model cars average( at most ) 30.20 miles per gallon for in-city driving.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.