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 = [tex]\frac{216.3-200}{16.3}[/tex]
∴ 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
#LearnwithBrainly
