Question

In: Statistics and Probability

The final exam grade of a mathematics class has a normal distribution with mean of 81...

The final exam grade of a mathematics class has a normal distribution with mean of 81 and standard deviation of 6.6. If a random sample of 40 students selected from this class, then what is the probability that the average final exam grade of this sample is between 77 and 82? Answer: (keep 4 decimal places)

Expert Solution

Solution :

Given that,

mean = = 81

standard deviation = = 6.6

n = 40

=81

₌ / $\sqrt$ n = 6.6 $\sqrt$ 40 = 1.0435

P (77 < < 82)

P ( 77 - 81 / 1.0435) < ( - / ) < ( 82 - 81 / 1.0435)

P ( - 4 / 1.0435 < z < 1 / 1.0435 )

P (-3.83 < z < 0.96)

P ( z < - 0.259 ) - P ( z < -3.83)

Using z table

= 0.8315 - 0.0001

= 0.8314

Probability = 0.8314

orchestra answered 2 years ago

he final exam grade of a statistics class has a skewed distribution with mean of 78...

he final exam grade of a statistics class has a skewed distribution with mean of 78 and standard deviation of 7.8. If a random sample of 30 students selected from this class, then what is the probability that average final exam grade of this sample is between 75 and 80?

final exam scores in a mathematics course are normally distributed with a mean of 79 and...

final exam scores in a mathematics course are normally distributed with a mean of 79 and a standard deviation of 8. an exam score is 103 and the Z score is 3, what is the percentile

A professor of a introductory statistics class has stated that, historically, the distribution of final exam...

A professor of a introductory statistics class has stated that, historically, the distribution of final exam grades in the course resemble a normal distribution with a mean final exam mark of 60% and a standard deviation of 9%. (a) What is the probability that a randomly chosen final exam mark in this course will be at least 75%? (b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of...

The scores of fourth grade students on a mathematics achievement test follow a normal distribution with...

The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4. What is the probability that a single student randomly chosen form all those taking the test scores 80 or higher? What is the probability that the sample mean score of 64 randomly selected student is 80 or higher?

The TEST grade of a statistics class has a skewed distribution with mean of 79 and...

The TEST grade of a statistics class has a skewed distribution with mean of 79 and standard deviation of 8.2. If a random sample of 35 students selected from this class, then what is the probability that average TEST grade of this sample is between 76 and 82? Answer: (round to 4 decimal places) The average amount of water in randomly selected 16-ounce bottles of water is 15.87 ounces with a standard deviation of 0.55 ounces. If a random sample...

8) Scores on an exam have a normal distribution with a mean of 80 and a...

8) Scores on an exam have a normal distribution with a mean of 80 and a standard deviation of 12. a) Find the probability that a person would score above 90. b) Find the probability that a person would score between 75 and 85. c) Find the probability that a group of 7 people would have a mean score above 84. d) Find the score needed to be in the top 10% of the class.

The grade of statistics follows a normal distribution with a mean of 85 and a standard...

The grade of statistics follows a normal distribution with a mean of 85 and a standard deviation of 10. The instructor adopted a new teaching method this year, and would like to investigate whether there is an improvement in students’ average grade. Suppose the average grade from a sample of 36 students is 88, can we conclude that there is an improvement at the 5% significance level? A. Specify the null and alternative hypotheses. B. Determine the rejection region. C....

The final exam scores in a statistics class were normally distributed with a mean of 70...

The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored less than 55% on the exam?

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of size 25 is taken, which of the following is the probability that the sample average is between 41.40 and 45.63?

Final exam scores in a Math class with large number of students have mean 145 and...

Final exam scores in a Math class with large number of students have mean 145 and standard deviation 4.1. Provided the scores of this Final exam follow a normal distribution, what's the probability that a student scores below 145 OR above 157.3? Find the answer without using the LSND program. (Write the answer in decimals)