Using the <em>normal distribution and the central limit theorem</em>, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.
<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
.
- When two variables are subtracted, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances.
<h3>What is the mean and the standard error of the distribution of differences?</h3>
For each sample, they are given by:
For the distribution of differences, we have that:
The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, <u>one subtracted by the p-value of Z when X = 0</u>, hence:
By the Central Limit Theorem
has a p-value of 0.0335.
1 - 0.0335 = 0.9665.
More can be learned about the <em>normal distribution and the central limit theorem</em> at brainly.com/question/24663213
Answer:
The correct answer is x = -13/5.
Step-by-step explanation:
To solve this problem, we need to bring all of the x terms to one side of the equation and all of the constant terms to the other side of the equation.
First, we should subtract x from both sides to cancel out the positive x on the left side of the equation. This is modeled below:
x - 13 = 6x
x - x - 13 = 6x - x
- 13 = 5x
Next, we should divide both sides by 5 in order to get the variable x completely isolated on the right side of the equation.
-13/5 = 5x/5
-13/5 = x
Therefore, your answer is x = -13/5.
Hope this helps!
Let x be the number of defective cell phones. It is given that in batch of 100, on average 5 are defective.
let p be the probability of defective cell phone.
p = 5/100 = 0.05
Let n be size of random sample, n=30
Here out of 30 we want to find probability that 2 will be defective. It means 30-2 =28 cell phones will be non defective.
The probability of getting non defective cell phone is 1- p=1-0.05 =0.95
The probabability of getting 2 defective is
P(X=2) = number of ways selecting 2 from 30 * probability 2 defective * probability of 28 non defective
Now number of ways of selecting 2 cell phone from 30 is
30C2 = 
= 
= 
= (30*29) /2
30C2 = 435
P(X=2) = 30C2 * (0.05)^2 * (0.95)^28
= 435 * 0.0025 * 0.2378
P(X=2) = 0.2586
Probability of getting 2 defective out of 30 is 0.2586
Answer:
about 13$ and 6 cents
Step-by-step explanation:
