Using the normal distribution, it is found that there is a 0.0013 = 0.13% probability that the mean weight of 25 pods of coffee is less than 42.035 grams.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters are given as follows:
![\mu = 42.05, \sigma = 0.025, n = 25, s = \frac{0.025}{\sqrt{25}} = 0.005](https://tex.z-dn.net/?f=%5Cmu%20%3D%2042.05%2C%20%5Csigma%20%3D%200.025%2C%20n%20%3D%2025%2C%20s%20%3D%20%5Cfrac%7B0.025%7D%7B%5Csqrt%7B25%7D%7D%20%3D%200.005)
The probability that the mean weight of 25 pods of coffee is less than 42.035 grams is the <u>p-value of Z when X = 42.035</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{42.035 - 42.05}{0.005}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B42.035%20-%2042.05%7D%7B0.005%7D)
Z = -3
Z = -3 has a p-value of 0.0013.
0.0013 = 0.13% probability that the mean weight of 25 pods of coffee is less than 42.035 grams.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
a=-14
Step-by-step explanation:
hope this helps
Answer: Nothing multiplies to 40 and adds to -6, it is impossible
12:45Answer:
Part A: 9 hours 45 minutes
Part B: $126.1575
Step-by-step explanation:
Part A,
From 7:45 to 12:15 is 4 hours and 30 minutes
From 12:45 which he clocked back in to 6:00 is 5 hours and 15 minutes.
4 hours and 30 minutes plus 5 hours and 15 minutes = 9 hours and 45 minutes.
Part B, 9 hours and 45 minutes can be represented as 9.45
And since he gets 15.35 "per" hour shows we can multiply.
15.35 x 9.45 = 126.1575
Therefor he earned 126.15.
1/5 of 500 is 100. 500 - 100 leaves 400 sheets of paper.
to find 2/5 of the remaining 400 sheets divide 400/5 then multiply by 2
400/5= 80 x 2 = 160 sheets which is 2/5 of the remaining 400.