An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. the amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. what is the probability that a randomly selected apple will contain more than 2.50 ounces? .9525 .4525 .0475 .5474

The probability that randomly selected apple will contain more than juice is .

Further explanation:

Given:

The mean of apple juice is .

The standard deviation of apple juice is .

Calculation:

The random variable follow Normal distribution with parameter mean and variance.

Normal distribution is symmetric and it bell shaped curve.

Variance is square of standard deviation.

Variance =

Variance =

Variance =

Substitute for and for

The probability that randomly selected apple will contain more than can be calculated by applying the central Limit Theorem as,

The Normal distribution is symmetric.

Therefore, the probability of greater than is equal to the probability of less than .

Hence, the probability that randomly selected apple will contain more than juice is .

Learn More:

1. Learn more about Unit conversion link

2. Learn more about Range of a function link

3. Learn more about Graph representation link

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Probability and Statistics

Keywords:

Probability, Statistics, Apple juice, Normal distribution, Normal approximation, Central Limit Theorem, Z-table, Mean, Standard deviation, Symmetric, Variance, Conglomerate of Apple, Northwestern.

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