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Chapter 5: Q 107. (page 333)

BMI (2.2) People with BMI less than 18.5 are often classed as “underweight.” What percent of young women are underweight by this criterion? Sketch and shade the area of interest under a Normal curve.

Short Answer

Expert verified

P (X < 18.5) = 13.14%

Step by step solution

01

Step 1. Given Information

μ = 26.8

σ = 7.4

02

Step 2. Concept used

Conditional probability :PB/A=PAandBPA

03

Step 3. Calculation

The z-score is the difference between the mean and the standard deviation:

z=x−μσ=18.5−26.8/7.4≈−1.12

Using the normal probability, apply the definitional conditional probability:

P(X<18.5)=P(Z<−1.12)=0.1314=13.14%

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Most popular questions from this chapter

Find P(L). Interpret this probability in context.

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent survey, 50% of people aged 13 and older in the United States are addicted to email. To simulate choosing a random sample of

20people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a

time. A red card means that person is addicted to email; a black card means he isn’t. Continue until you have drawn 20cards (without replacement) for the sample.

(b) A tennis player gets 95%of his second serves in play during practice (that is, the ball doesn’t go out of bounds). To simulate the player hitting 5second serves, look at pairs of digits going across a row in Table D. If the number is between 00and 94, the service is in; numbers between 95and 99indicate that the service is out.

Sampling senators The two-way table below describes the members of the U.S Senate in a recent year. Male Female Democrats 4713 Republicans 364

(a) Who are the individuals? What variables are being measured?

(b) If we select a U.S. senator at random, what’s the probability that we choose

  • a Democrat?
  • a female?
  • a female Democrat?
  • a female or a Democrat?

Lotto In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry

out a simulation to answer this question. Follow the four-step process.

Monty Hall problem In Parade magazine, a reader posed the following question to Marilyn vos Savant and the “Ask Marilyn” column: Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a

goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors? The game show in question was Let’s Make a Deal and the host was Monty Hall. Here’s the first part of Marilyn’s response: “Yes; you should switch. The first door has a 1/3 chance of winning, but

the second door has a 2/3 chance.” Thousands of readers wrote to Marilyn to disagree with her answer. But she held her ground.

(a) Use an online Let’s Make a Deal applet to perform at least 50 repetitions of the simulation. Record whether you stay or switch (try to do each about half

the time) and the outcome of each repetition.

(b) Do you agree with Marilyn or her readers? Explain.
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