# statistics

Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. Estimate the probability that among 75 randomly selscted students, at least 20 of them score greater that 78.

1. 👍 0
2. 👎 0
3. 👁 163
1. Use z-scores.

z = (x - mean)/sd

z = (78 - 68.2)/10.4 = 0.94

.1736 is the probability using a z-table for a single student with a score greater than 78.

Now we can use a normal approximation to the binomial distribution.

mean = np = (75)(.1736) = 13
standard deviation = √np(1-p) = √(75)(.1736)(.8264) = 3.28

Again, use z-scores.
z = (20 - 13)/3.28 = 2.13

Use the z-table to find the probability. (Remember the problem says "at least 20" which means 20 or more.)

I hope this will help.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Word Problem

A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 25 and a standard deviation of 4.6. Scores on the second test are normally

asked by Lyndse on March 7, 2010
2. ### Statistics

Scores on an IQ test are normally distributed. A sample of 15 IQ scores had standard deviation s=10. The developer of the test claims that the population standard deviation is =15. Do these data provide sufficient evidence to

asked by steph on March 12, 2019
3. ### Algebra

The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.

asked by Anonymous on February 4, 2016
4. ### algebra

The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.

asked by Katie on January 28, 2015
5. ### Math

The scores of students on standardized test are normally distributed with a mean of 300 and a standard deviation of 40. Between what two values do 99.7% of the test scores lie?

asked by Nancy on March 1, 2014
6. ### stat

for randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. the scores of 14 randomly selected college students are listed below. use a 0.10 significance level to test the claim that the

asked by carl on May 14, 2012
7. ### Analytical Skills

If your score on a statistics exam was 76 and the professor gave you the distribution for the exam score for your class, you could find your percentile to understand where you stand in comparison to your fellow students. Assume

asked by Jojo on October 6, 2011
8. ### algebra 2 and trig

The scores on a chemistry test are normally distributed. Approximately 95 percent of the scores fell between 78 and 92. What is the standard deviation for this distribution?

asked by caroline on May 18, 2015
9. ### statistics

Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 25. Use the 68-95-99.7 rule to find the following quantities. The percentage of scores less than 80 is?

asked by nicole on May 24, 2011
10. ### Statistics Math Help

A distribution of 800 test scores in a biology course was approximately normally distributed with a mean of 35 and a standard deviation of 6. Calculate the proportion of scores falling between 20 and 40

asked by Fred on June 18, 2011
11. ### Statistics

A distribution of 800 test scores in a biology course was approximately normally distributed with a mean of 35 and a standard deviation of 6. Calculate the proportion of scores falling between 20 and 40

asked by Fred on June 18, 2011

More Similar Questions