Question

In a school with 1,000 students, the heights of students are normally distributed with a mean of 113 centimeters and a standard deviation of 5 centimeters. How many students are shorter than 121 centimeters?(1 point) Responses 55 55 945 945 950 950 445

Answer 1

To find out how many students are shorter than 121 centimeters in a normally distributed population, we can use the Z-score formula:

\[
Z = \frac{X - \mu}{\sigma}
\]

where:
- \(X\) is the value we are interested in (121 cm),
- \(\mu\) is the mean (113 cm),
- \(\sigma\) is the standard deviation (5 cm).

Now plug in the values:

\[
Z = \frac{121 - 113}{5} = \frac{8}{5} = 1.6
\]

Next, we will look up the Z-score of 1.6 in the standard normal distribution table or use a calculator to find the probability corresponding to this Z-score.

The cumulative probability for \(Z = 1.6\) is approximately 0.9452. This means that about 94.52% of students are shorter than 121 centimeters.

Now we can calculate the number of students shorter than 121 cm in a school of 1,000 students:

\[
0.9452 \times 1000 \approx 945.2
\]

Since we can't have a fraction of a student, we round this to 945.

Therefore, the number of students shorter than 121 centimeters is approximately **945**.