Using the normal distribution, it is found that 0.26% of the items will either weigh less than 87 grams or more than 93 grams.
In a <em>normal distribution</em> 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.
In this problem:
- The mean is of 90 grams, hence
.
- The standard deviation is of 1 gram, hence
.
We want to find the probability of an item <u>differing more than 3 grams from the mean</u>, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{3}{1}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B3%7D%7B1%7D)
![Z = 3](https://tex.z-dn.net/?f=Z%20%3D%203)
The probability is P(|Z| > 3), which is 2 multiplied by the p-value of Z = -3.
- Looking at the z-table, Z = -3 has a p-value of 0.0013.
2 x 0.0013 = 0.0026
0.0026 x 100% = 0.26%
0.26% of the items will either weigh less than 87 grams or more than 93 grams.
For more on the normal distribution, you can check brainly.com/question/24663213
Answer:
0.11
Step-by-step explanation:
Answer:
D!
Step-by-step explanation:
Answer:
Answer: The mean increases by 3
Step-by-step explanation:
The original data set is
{50, 76, 78, 79, 79, 80, 81, 82, 82, 83}
The outlier is 50 because it is not near the group of values from 76 to 83 which is where the main cluster is.
The original mean is M = (50+76+78+79+79+80+81+82+82+83)/10 = 77
If we take out the outlier 50, the new mean is N = (76+78+79+79+80+81+82+82+83)/9 = 80
So in summary so far
old mean = M = 77
new mean = N = 80
The difference in values is N-M = 80-77 = 3
So that's why the mean increases by 3
Answer:
Average cost per ball: $22.2
Step-by-step explanation:
Cost per ball: $22
Cost of 300 balls: 300 × 22 = $6600
Total No. of Orders: 3
Delivery fee per order: $20
Total Delievery fee: 20 × 3 =$60
Total cost including delivery cost: $6600 + $60 = $6660
![Average cost per ball = \frac{Total cost}{No. of balls}](https://tex.z-dn.net/?f=Average%20cost%20per%20ball%20%3D%20%5Cfrac%7BTotal%20cost%7D%7BNo.%20of%20balls%7D)
![Average cost per ball = \frac{6660}{300}](https://tex.z-dn.net/?f=Average%20cost%20per%20ball%20%3D%20%5Cfrac%7B6660%7D%7B300%7D)
![Average cost per ball = $22.2](https://tex.z-dn.net/?f=Average%20cost%20per%20ball%20%3D%20%2422.2)