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Chapter 7: Q 50. (page 464)

In a congressional district, 55% of the registered voters are Democrats. Which of the following is equivalent to the probability of getting less than 50% Democrats in a random sample of size 100?

a. P(z<0.50−0.55100)

b. P(z<0.50−0.550.55(0.45)100)

c. P(z<0.55−0.500.55(0.45)100)

d. P(z<0.50−0.55100(0.55)(0.45))

e. P(z<0.55−0.50100(0.55)(0.45))

Short Answer

Expert verified

The correct option is (b) pz<0.50−0.550.55×0.45100

Step by step solution

01

Given information

p=0.55p^=0.50n=100

02

Concept

σp^=p(1−p)n

03

Calculation

μp^=p=0.55σp^=p(1−p)n=0.55(1−0.55)100=0.55×0.45100z=x−μσ=0.50−0.550.55×0.45100

The sample proportion must be less than 50% with a probability of less than 50%

p(p^<50%)=pz<0.50−0.550.55×0.45100

Hence, the correct option is (b)

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Most popular questions from this chapter

Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ=298mland standard deviation σ=3ml.

a. What is the probability that a randomly selected bottle contains less than 295ml?

b. What is the probability that the mean contents of six randomly selected bottles is less than 295ml?

A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.

a. Without doing any calculations, explain which event is more likely:

  • randomly selecting 1 car entering this interchange during rush hour and finding 2 or more people in the car
  • randomly selecting 35 cars entering this interchange during rush hour and finding an average of 2 or more people in the cars

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).

Fillings How much do prices vary for filling a cavity? To find out, an insurance company randomly selects 10dental practices in California and asks for the cash (non-insurance) price for this procedure at each practice. The interquartile range is $74.

More sample proportions List all 4possible SRSs of size n=3, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dot plot with the same scale as the dot plot in Exercise 19. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise 19? What does this indicate about increasing the sample size?

From exercise19:

Car NumberColorAge
1
Red
1
2
White
5
3
Silver
8
4
Red
20

At a particular college, 78%of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100students and 72%of the respondents say they are receiving some sort of financial aid. Which of the following is true?

  1. 78%is a population and 72%is a sample.
  2. 72%is a population and 78%is a sample.
  3. 78%is a parameter and 72%is a statistic.
  4. 72%is a parameter and 78%is a statistic.
  5. 72%is a parameter and 100is a statistic.
See all solutions

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