Question

A plant biologist is interested in studying the height of sunflowers. he measures a large sample of sunflowers and determines that their height is approximately normally distributed with mean 112 cm and standard deviation 16 cm. (a) what is the probability (approximately) that a sunflower will be less than 115 cm tall? sketch the area corresponding to this probability.

Answer 1

The probability that a sunflower will be less than 115 cm tall is approximately 0.5745.

How to find the probability

To find the probability that a sunflower will be less than 115 cm tall, use the standard normal distribution and z-scores.

First, calculate the z-score for 115 cm using the formula:

z = (x - μ) / σ

where

x is the value we want to find the probability for (115 cm),

μ is the mean (112 cm), and

σ is the standard deviation (16 cm).

z = (115 - 112) / 16

z ≈ 0.1875

Next, use a standard normal distribution table or a statistical calculator to find the probability corresponding to the z-score of 0.1875.

Using a standard normal distribution table, find the cumulative probability associated with the z-score of 0.1875.

The table provides the area to the left of the z-score.

The cumulative probability for a z-score of 0.1875 is approximately 0.5745.

So, the probability that a sunflower will be less than 115 cm tall is approximately 0.5745.

To sketch the area corresponding to this probability, you can draw a normal distribution curve and shade the area to the left of the value 115 cm.

The shaded area represents the probability of a sunflower being less than 115 cm tall.

Attached is the normal distribution curve.