Question

In: Statistics and Probability

The marks on a statistics midterm test are normally distributed with a mean of 75 and...

The marks on a statistics midterm test are normally distributed with a mean of 75 and a standard deviation of 6. What is the probability that a sample of 50 exams has a sample mean between 74 and 75?

a. 0.3810

b. 0.1210

c. 0.4641

d. 0.3790

e. 0.1190

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 75

standard deviation = =   6

n = 50

= 75

=  / n= 6 / 50=0.849

P(74<     < 75) = P[(74-75) / 0.849< ( - ) /   < (75-75) /0.849 )]

= P( -1.18< Z <0 )

= P(Z <0) - P(Z < -1.18)

Using z table

=0.5 -0.1190

PROBABILITY =0.3810

orchestra answered 3 years ago
Next > < Previous

Related Solutions

The marks on a statistics midterm test are normally distributed with a mean of 75 and...
The marks on a statistics midterm test are normally distributed with a mean of 75 and a standard deviation of 6. What is the probability that a sample of 50 exams has an average midterm test mark that is less than 70? a. Virtually 0 b. 0.2033 c. -5.89 d. 0.2776 e. Virtually 1
The marks on a statistics midterm test are normally distributed with a mean of 75 and...
The marks on a statistics midterm test are normally distributed with a mean of 75 and a standard deviation of 6. What is the probability that a sample of 25 exams has a sample mean between 71 and 73? a. 0.45293 b. 0.04793 c. 0.0475 d. 0.0485 e. 0.04707
A sample of midterm test results is distributed normally where the mean = 77 and the...
A sample of midterm test results is distributed normally where the mean = 77 and the variance = 12. 1. What percentage of these scores is between 70 and 80? 2. What raw score is the cutoff for the top 10% of scores? 3. What is the probability of obtaining a score lower than 70? 4. What is the probability of obtaining a score greater than 90?
The scores on a statistics test are Normally distributed with parameters µ = 75 and σ...
The scores on a statistics test are Normally distributed with parameters µ = 75 and σ = 10. Find the probability that a randomly chosen score is (a) no greater than 60 (b) at least 90 (c) between 60 and 90 (d) between 65 and 85 (e) at least 75
The final marks in a statistics course are normally distributed with a mean of 70 and...
The final marks in a statistics course are normally distributed with a mean of 70 and a variance of 100. The professor must convert all marks to letter grades. He decides that he wants 10% A's, 30% B's, 40% C's, 15% D's and 5% F's. Determine the cutoffs for each letter grade.
Scores of students in a large Statistics class are normally distributed with a mean of 75...
Scores of students in a large Statistics class are normally distributed with a mean of 75 points and a standard deviation of 5 points. Find the probability that a student scores more than 80 points If 100 students are picked at random, how many do you expect to score below 70 points? If top 10% of students obtain an A grade, how much should a student obtain to get an A grade. Suppose four students are picked at random, find...
Suppose the mean grade for a statistics midterm exam was 75, with a standard deviation of...
Suppose the mean grade for a statistics midterm exam was 75, with a standard deviation of 10. Assume that your grades were normally distributed. a. What percentage of students received at least an 90? e. If 2 students failed the exam, i.e. their grades were less than 60, how many students took the test? Hint: First focus on p(x<60).
Suppose the scores earned on a statistics test are normally distributed with a mean of 65...
Suppose the scores earned on a statistics test are normally distributed with a mean of 65 and a standard deviation 8. The instructor wants to curve the test scores as follows: The top 5% get an A, the next 20% get a B, the middle 50% get a C, the bottom 10% get an F, and the rest earn a D. Determine the score cutoffs for the test.
The grades on a statistics test are normally distributed with a mean of 62 and Q1=52....
The grades on a statistics test are normally distributed with a mean of 62 and Q1=52. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher? Please round your answer to two decimal places. The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For...
Suppose that the midterm score of a class is normally distributed with the mean of 68.2...
Suppose that the midterm score of a class is normally distributed with the mean of 68.2 points and the standard deviation of 11.3 points. Answer each question. (5 pts) Sketch the curve of the distribution representing the midterm score. Make sure to mark the mean and three standard deviations to either side of the mean. (10 pts) Find the probability that a randomly selected student has score at most 65.9 (10 pts) To be in the top 20% of the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT