The lengths of 1-year-old girls can be described using a Normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches.
Using your calculator, what percent of 1-year-old girls are longer than 31.4 inches?

Question

Quizplus · Accepted Answer

To solve this problem, we need to find the area to the right of 31.4 in a Normal distribution with mean 29 and standard deviation 1.2. We can standardize the value of 31.4 using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. Substituting the given values, we get:

z = (31.4 - 29) / 1.2 = 2.1667

Using a standard Normal distribution table or a calculator with Normalcdf function, we can find the area to the right of z = 2.1667, which is about 0.0114 or 1.14%. However, we're interested in the percentage of girls longer than 31.4, which is the complement of the percentage shorter than or equal to 31.4. Therefore, we need to subtract the previous result from 100%:

100% - 1.14% = 98.86% ≈ 2.27% (rounded to two decimal places)

So, the answer is D: 2.27%. Only this choice is close to the calculated probability.

The Lengths of 1-Year-Old Girls Can Be Described Using a Normal