Question

A manufacturer of cereal finds that the masses of cereal in the company's 200-g packages are normally distributed with a mean of 200 g and a standard deviation of 16.3 g. What is the probability that a box selected at random contains more than 216.3 g of cereal?​

Answer 1

The probability that the box selected at random contains more than 216.3 g of cereal is 0.15866

Step-by-step explanation:

A manufacturer of cereal finds that the masses of cereal in the company's 200-g packages are normally distributed

• The mean is 200 g
• The standard deviation is 16.3

We need to find the probability that a box selected at random contains more than 216.3 g of cereal

To find the probability let use find z-score

∵ z-score = (X - μ)/σ, where x is the random variable, μ is the mean

   and σ is the standard deviation

∵ μ = 200 g

∵ σ = 16.3 g

∵ X = 216.3 g

- Substitute these values in the rule of z-score

∴ z-score = $\frac{216.3-200}{16.3}$

∴ z-score = 1

For probability that X > 216.3 use the normal distribution table to find the area corresponding to the right z-score = 1

∵ The area corresponding to z-score to the left = 0.84134

∴ The area corresponding to z-score to the right = 1 - 0.84134

∴ The area corresponding to z-score to the right = 0.15866

∴ P(X > 216.3) = 0.15866

The probability that the box selected at random contains more than 216.3 g of cereal is 0.15866

Learn more:

You can learn more about z-score in brainly.com/question/6270221

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