Question

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490 and 500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 25 students. What is the standard deviation of the sampling distribution of their average score ?¯? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490 and 500 ? (Enter your answer rounded to four decimal places.)

probability:

STATE: How heavy a load (in pounds) is needed to pull apart pieces of Douglas fir 44 inches long and 1.51.5 inches square? Given are data from students doing a laboratory exercise.

33,190	31,860	32,590	26,520	33,280
32,320	33,020	32,030	30,460	32,700
23,040	30,9303	32,720	33,650	32,340
24,050	30,170	31,300	28,730	31,920

To access the complete data set, click the link for your preferred software format:

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We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume that characteristics of materials vary Normally. Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds.

PLAN: We will estimate μ by giving a 90% confidence interval.

SOLVE: Find the sample mean ?¯ . (Enter your answer rounded to the nearest whole number.)

?¯=

Give a 90% confidence interval, [low,high] , for the mean load required to pull the wood apart. (Enter your answers rounded to the nearest whole number.)

???=

ℎ??ℎ=

Answer 1