Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
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
.
- The standard deviation is of
.
- Sample of 100, hence

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:
Z = -2:

By the Central Limit Theorem




Z = 2:




The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).
You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213
x - y = 14
given the ratio x : y = 5 : 3
then let x = 5x and y = 3x, hence equation can be expressed as
5x + 3x = 56
8x = 56 ( divide both sides by 8 )
x = 7
Hence x = 5 × 7 = 35 and y = 3 × 7 = 21
Thus x - y = 35 - 21 = 14
Answer: 4545
Step-by-step explanation:
Split the summation into smaller summations that fit the summation rules.
Step-by-step explanation:
They are equal because when we flip or reflect ABC onto DCB we are going to have the same size and the same shape

<em>Convert the mixed number to the improper fraction.</em>

