Question

A particular fruit's weights are normally distributed, with a mean of 311 grams and a standard deviation of 15 grams.

If a fruit is picked at random then 5% of the time, its weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

Solution :

Let X be a random variable which represents the particular fruit's weight.

Given that,  

Mean (μ) = 311 grams

Standard deviation (σ) = 15 grams

Let, if a fruit is picked at random then 5% of the time, its weight will be greater than k grams.

Hence, P(X > k) = 0.05

We know that, if X ~ N(μ, σ²) then,

......................(1)

Using "qnorm" function of R we get, P(Z > 1.645) = 0.05

Comparing, P(Z > 1.645) = 0.05 and (1) we get,

Hence, if a fruit is picked at random then 5% of the time, its weight will be greater than 335.7 grams.