A particular fruit's weights are normally distributed, with a mean of 701 grams and a standard deviation of 30 grams. If you pick 24 fruits at random, then 2% of the time, their mean weight will be greater than how many grams?
A particular fruit's weights are
If you pick 24 fruits at random, then 2% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
![](/static/compass_v2/shared-icons/check-mark.png)
It is given that the fruit weights have a normal distribution with mean 701 grams and standard deviation 30 grams.
Denote the random variable X as the fruit weight of a randomly selected fruit.
That is, µ= 701, σ= 30.
Sampling distribution of the sample mean:
By central limit theorem, the mean of the sampling distribution is μx-bar = 701.
The population standard deviation is, σ =30. The sample size is, n = 24.
The standard deviation using central limit theorem is σ/√n= 30/√24= 6.124.
Thus, the sampling distribution of the sample mean for sample of size 24 follows normal distribution with mean μx-bar = 701 and standard deviation 6.124.
x-bar ~N(701,6.124).
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)