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.
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).
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