Question

The population of weights of a particular fruit is normally distributed, with a mean of 535 grams and a standard deviation of 13 grams. If 8 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Answer 1

Pn(Z>zp)=1−p%

Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a

is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:

$z=\frac{x-\mu}{\sigma}$

The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.

The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.

Pn(Z>zp)=1−p%

Here Pn is the probability for the standard normal variable.

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