Answered

Find expert answers and community-driven knowledge on IDNLearn.com. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.

Question content area top
Part 1
In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.4 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.
Question content area bottom
Part 1
​(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is

Sagot :

Thetawnyytidn
Final answer:
The probability that the study participant selected at random is less than 68 inches tall is approximately 0.4602.

Explanation:
To find this probability, we use the z-score formula for a normal distribution. Given the mean height of 68.4 inches and a standard deviation of 4.0 inches, we calculate the z-score for 68 inches:
\[ z = \frac{68 - 68.4}{4.0} = -0.1 \]
Using a standard normal distribution table or calculator, the cumulative probability corresponding to a z-score of -0.1 is about 0.4602. Thus, the probability that a randomly selected participant is shorter than 68 inches is 0.4602, or 46.02%.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.