Question

A particular fruit's weights are normally distributed, with a mean of 341 grams and a standard

deviation of 18 grams.
If you pick 4 fruit at random, what is the probability that their mean weight will be between 349
grams and 366 grams?

Answer 1

The distribution of the sample mean of four fruits is also normal with a mean of 341 g and a standard deviation of 18 g divided by the square root of 4, which is 9 g.

Let X be the weight of a single fruit, then we want to find the probability that the sample mean, M, is between 349 g and 366 g:

Z1 = (349 - 341) / 9 = 0.89

Z2 = (366 - 341) / 9 = 2.78

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(0.89 < Z < 2.78) = 0.4599 - 0.1867 = 0.2732

Therefore, the probability that the mean weight of 4 fruits will be between 349 g and 366 g is approximately 0.2732 or 27.32%.

Answer 2

the probability that the mean weight of 4 randomly picked fruits falls between 349 grams and 366 grams is approximately 0.0902, or 9.02%.