When women were finally allowed to become pilots of fighter​ jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 150 lb and 201 lb. Weights of women are now normally distributed with a mean of 174 lb and a standard deviation of 42 lb. Complete parts​ (a) through​ (c) below.
Question content area bottom
Part 1
a. If 1 woman is randomly​ selected, find the probability that her weight is between 150 lb and 201 lb.
The probability is approximately

enter your response here. ​(Round to four decimal places as​ needed.)

The probability that a randomly selected woman's weight is between 150 lb and 201 lb is approximately 0.4560 (rounded to four decimal places).

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How would the probability change if the standard deviation was smaller?
2. What is the probability of selecting a woman whose weight is less than 150 lb?
3. If the weight limits were changed to 140 lb and 210 lb, how would the probability be affected?
4. What is the probability of selecting a woman weighing more than 201 lb?
5. How could the redesign of the ejection seats take into account the variability in women's weights?

**Tip:** Understanding the concept of Z-scores is key to finding probabilities in a normal distribution, as they measure how far a data point is from the mean in terms of standard deviations.

When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 150 lb and 201 lb. Weights of women are now normally distributed with a mean of 174 lb and a standard deviation of 42 lb. Complete parts (a) through (c) below. Part 1: a. If 1 woman is randomly selected, find the probability that her weight is between 150 lb and 201 lb.

Find the probability that a randomly selected woman weighs between 150 lb and 201 lb, given a normal distribution with a mean of 174 lb and a standard deviation of 42 lb. This problem covers key statistical concepts such as Z-scores and probability in normal distributions, ideal for students in Grades 11-12 and college-level statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation