Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:

- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of 660, hence
.
- The standard deviation is of 90, hence
.
- A sample of 100 is taken, hence
.
The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

By the Central Limit Theorem



has a p-value of 0.8665.
1 - 0.8665 = 0.1335.
0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213
Answer:
1197.9
Step-by-step explanation:
10 percent of 1331 is 133.1.
because its 10 percent more, you need to do 1331-133.1:)
Answer:
The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%
Step-by-step explanation:
For a normal random variable with mean Mu = 3.2 and standard deviation sd = 0.8 there is a distribution of the sample mean (MX) for samples of size 4, given by:
Z = (MX - Mu) / sqrt (sd ^ 2 / n) = (MX - 3.2) / sqrt (0.64 / 4) = (MX - 3.2) / 0.4
For a sample mean of 3.0, Z = (3 - 3.2) / 0.4 = -0.5
For a sample mean of 3.0, Z = (4 - 3.2) / 0.4 = 2.0
P (3.2 <MX <4) = P (-0.5 < Z <2.0) = 0.6687.
The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%
A.25
Work:
-5x-5=25
Hope his helps.