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lorasvet [3.4K]
3 years ago
7

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.2 grams with a standard deviat

ion of 0.18 grams. Enter your responses as a decimal with 4 decimal places. (a) What is the probability that a randomly chosen mouse has a mass of less than 19.99 grams?
Mathematics
1 answer:
Sophie [7]3 years ago
6 0

Answer:

12.1%

Step-by-step explanation:

Given that:

Mean (μ) = 20.2 grams and standard deviation (σ) = 0.18 grams.

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean. A positive z score means  that the raw score is above the mean and a negative z score means that the raw score is below the mean. It is given by:

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

a) For x < 19.99 g:

z=\frac{x-\mu}{\sigma}\\\\z=\frac{19.99-20.2}{0.18} \\\\z=-1.17

From the normal distribution table, P(x < 19.99) = P(z < -1.17) = 0.1210 = 12.1%

The probability that a randomly chosen mouse has a mass of less than 19.99 grams is 12.1%

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