Question

In: Statistics and Probability

10. The grades of students are normal distributed. In a class of 10 students the average...

10. The grades of students are normal distributed. In a class of 10 students the average grade on a quiz is 16.35, with a standard deviation of 4.15. ( 3 marks ) a) Find the 90% confidence interval for the population mean grade. b) If you wanted a wider confidence interval, would you increase or decrease the confidence level?

Expert Solution

Given that,

= 16.35

s =4.15

n = 10

Degrees of freedom = df = n - 1 = 10- 1 = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,9 = 1.833 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 1.833 * ( 4.15/ $\sqrt$ 10) = 2.4055

The 90% confidence interval estimate of the population mean is,

- E < < + E

16.35 - 2.4055< <16.35 + 2.4055

13.9445 < < 18.7555

( 13.9445 , 18.7555)

(B) increase

orchestra answered 1 year ago

A set of final grades in an introductory probability class in section A is normal distributed...

A set of final grades in an introductory probability class in section A is normal distributed with mean 70 and standard deviation of 10 : G1 ~ N (70,100). a) what is probability that grade of randomly chosen student is 77 or less? b)what is probability that average grade of 9 randomly chosen students is 77 or less? c) only 2% of the students scored higher that what grade? d) A set of final grades in an introductory probability class...

An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's,...

An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. At the end of the semester, she has the following grades. A 12B 20C 25D 13F 5 Test her claim at 1% significance level.

The grades of a group of 1000 students in an exam are normally distributed with a...

The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student is randomly selected from the group. Find the probability that; a. Their grade is greater than 80 b. Their grade is less than 50 c. That their grade is between 50 and 80 d. Approximately, how many students have grade greater than 80% and how many have less than 50%

The grades of a class of 9 students on a midterm report (x) and on the...

The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: x 77 50 71 72 81 94 96 99 67 y 82 66 78 34 47 85 99 99 68 Compute a 95% confidence interval for the mean response mu subscript Y divided by x end subscript when x equals 85.

A class consisting of 10 students takes a test. The scores are approximately normally distributed with...

A class consisting of 10 students takes a test. The scores are approximately normally distributed with a mean of 74 and a standard deviation of 11. The teacher wants to curve the grades in the following manner: the top 5% get As, the next highest 12% get Bs, the bottom 5% get Fs, and the next lowest 12% get Ds. The rest will get Cs. Find the Z-scores for each line and the test score corresponding to each z score

A teacher hypothesizes that the final grades in her class (N = 54) are distributed as...

A teacher hypothesizes that the final grades in her class (N = 54) are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. At the end of the semester, she has the following grades: A B C D F 6 14 22 8 4 Considering the statement above, what are the expected frequencies for grades A and F respectively?

Suppose that the final grades in a stats course are approximately Normally distributed, with an average...

Suppose that the final grades in a stats course are approximately Normally distributed, with an average grade of 83 and a SD of 5. A student is randomly selected. a.) what is the probability that the selected student received an A (at least 90)? b.) the students know that their final grade is at the 81st percentile. Show whether or not that students grade is an A. c.) if the students final grade is a least a B-, what is...

Exam grades: Scores on a statistics final in a large class were normally distributed with a...

Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 70 and a standard deviation of 10. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 42nd percentile of the scores. (b) Find the 71st percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 10% of the class. What...

The test grades in some class follow a normal distribution (we will call it X) with...

The test grades in some class follow a normal distribution (we will call it X) with σ = 8. Use this information (and the chart!) to answer the following questions: (a) If there is a 60% chance that a student scores higher than a 75, find µ, the average test grade for this class. (b) Using the µ you found in part (a), determine P(72 ≤ X ≤ 90).

An instructor gives a 100 point exam which grades are normal distributed. the mean is 66...

An instructor gives a 100 point exam which grades are normal distributed. the mean is 66 and the standard deviation is 8. If there are 12% A, 10% B, 60% C, 10% D, and %8 F. find the scores and then divide the distribution into those categories. Suppose 50 students were selected from a class who took the exam in the above problem. What is the probability the class average was a 65 and a 67?