Question

Heights of boys in a high school are approximately normally distributed with mean of 175 cm and standard deviation of 5 cm. what is the first quartile of heights

Answer 1

The first quartile of heights for boys in the high school is approximately 171.6 cm, calculated using the z-score for the 25th percentile of a normal distribution and the provided mean and standard deviation.

Step-by-step explanation:

To find the first quartile (Q1) of heights for boys in a high school where the heights follow a normal distribution with a mean of 175 cm and a standard deviation of 5 cm, we need to determine the height below which 25% of the data falls. The first quartile corresponds to the 25th percentile of the distribution.

Using the standard normal distribution table or a calculator with the inverse cumulative distribution function for a normal distribution, we find the z-score that corresponds to the 25th percentile. This z-score is approximately -0.6745.

Then, we convert the z-score to a height using the formula:

• Q1 = mean + (z-score × standard deviation)

Therefore:

• Q1 = 175 cm + (-0.6745 × 5 cm)

Q1 = 175 cm - 3.3725 cm

Q1 ≈ 171.6 cm

Thus, the first quartile of heights for these boys is approximately 171.6 cm.

Answer 2

The first quartile of heights for boys in a high school, with a mean of 175 cm and standard deviation of 5 cm, is approximately 171.63 cm. This is found using the z-score for the 25th percentile in a standard normal distribution and converting it to height.

Step-by-step explanation:

The first quartile of heights for boys in a high school, which are approximately normally distributed with a mean of 175 cm and standard deviation of 5 cm, can be found by looking up the z-score that corresponds to the 25th percentile in a standard normal distribution table. This z-score is approximately -0.674. To convert this z-score to a height, use the formula:
x = μ + (z × σ), where x is the height corresponding to the first quartile, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
x = 175 + (-0.674 × 5) = 171.63 cm.