1ugcz
Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

The weights of 1500 bodybuilders are normally distributed with a mean of 190.6 pounds and a standard deviation of 5.8 pounds.

A. About how many bodybuilders are between 180 and 190 pounds?

B. What is the probability that a bodybuilder selected at random has a weight greater than 195 pounds?

Sagot :

semsee45

Answer:

A.  637

B.  0.2240 (4 dp) = 22.4% (nearest tenth)

Step-by-step explanation:

Normal Distribution

[tex]\sf X \sim N(\mu, \sigma^2)[/tex]

Given:

  • [tex]\sf \mu = 190.6[/tex]
  • [tex]\sf \sigma=5.8[/tex]

[tex]\implies \sf X \sim N(190.6, 5.8^2)[/tex]

Part A

[tex]\begin{aligned}\sf P(180 < X < 190) & = \sf P(X < 190)-P(X\leq 180)\\& = \sf 0.4588035995-0.03380583874\\& = \sf 0.4249977608\end{aligned}[/tex]

Total number of bodybuilders = 1500

Therefore, the number of bodybuilders between 180 and 190 pounds is:

[tex]\begin{aligned}\sf P(180 < X < 190) \cdot1500 & = \sf 0.4249977608 \cdot 1500\\& = \sf 637.4966412\\& = \sf 637\end{aligned}[/tex]

Part B

[tex]\begin{aligned}\sf P(X > 195) & = \sf 1-P(X\leq 195)\\& = \sf 1-0.7759602537\\ & = \sf 0.2240397463\\ & = \sf 0.2240\:(4\:dp)\end{aligned}[/tex]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.