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Chapter 5: 5-50E (page 321)

Question:Who prepares your tax return? As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers found that 37% of adult workers prepare their own tax return. Assume that this percentage applies to all U.S. adult workers. Now consider a random sample of 270 adult workers.

a. Find the probability that more than 112 of the workers prepare their own tax return.

b. Find the probability that between 100 and 150 of the workers prepare their own tax return

Short Answer

Expert verified
  1. The probability that more than 112 of the workers prepare their own tax return is zero.
  2. The probability that between 100 and 150 of the workers prepare their own tax return is zero.

Step by step solution

01

Given Information

The proportion of adult workers is given by

The number of sample size is

The standard deviation of the sampling distribution is computed as

σp^=p1-pn=0.37×0.63270=0.0017

So, p^ is normally distributed with mean of 0.37 and a standard deviation of 0.0017.

02

(a) Compute the probability

The probability that more than 112 of the workers is computed as

03

(b) Identifying the probability

The probability that between 100 and 150 of the workers is computed as

100<p^<150=p100-0.370.0017<p^-pσp^<150-0.370.0017=p58605.88<z<88017.64=pz⩽88017.64-pz⩽58605.88=1-1=0

Hence, the probability is 0.

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Most popular questions from this chapter

Refer to Exercise 5.18. Find the probability that

  1. x¯is less than 16.
  2. x¯is greater than 23.
  3. x¯is greater than 25.
  4. x¯falls between 16 and 22.
  5. x¯ is less than 14.

Video game players and divided attention tasks. Human Factors (May 2014) published the results of a study designed to determine whether video game players are better than non–video game players at crossing the street when presented with distractions. Participants (college students) entered a street-crossing simulator. The simulator was designed to have cars traveling at various high rates of speed in both directions. During the crossing, the students also performed a memory task as a distraction. The researchers found that students who are video game players took an average of 5.1 seconds to cross the street, with a standard deviation of .8 second. Assume that the time, x, to cross the street for the population of video game players has , Now consider a sample of 30 students and let x represent the sample mean time (in seconds) to cross the street in the simulator.

a. Find Px¯>5.5

b. The 30 students in the sample are all non–video game players. What inference can you make about and/or for the population of non–video game players? Explain.

Switching banks after a merger. Banks that merge with others to form “mega-banks” sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First Union, a random sample of 250 retail customers who had banked with First Fidelity were questioned. Letp^ be the proportion of those customers who switched their business from First Union to a different bank.

  1. Find the mean and the standard deviation of role="math" localid="1658320788143" p^.
  2. Calculate the interval Ep^±2σp^.
  3. If samples of size 250 were drawn repeatedly a large number of times and determined for each sample, what proportion of the values would fall within the interval you calculated in part c?

Question:Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). The researchers found that the probability of a Finnish citizen investing in the stock market differed depending on IQ score. For those with a high IQ score, the probability is .44; for those with an average IQ score, the probability is .26; and for those with a low IQ score, the probability is .14.

a. In a random sample of 500 Finnish citizens with high IQ scores, what is the probability that more than 150 invested in the stock market?

b. In a random sample of 500 Finnish citizens with average IQ scores, what is the probability that more than 150 invest in the stock market?

c. In a random sample of 500 Finnish citizens with low IQ scores, what is the probability that more than 150 invest in the stock market?

Analysis of supplier lead time. Lead timeis the time betweena retailer placing an order and having the productavailable to satisfy customer demand. It includes time for placing the order, receiving the shipment from the supplier, inspecting the units received, and placing them in inventory. Interested in average lead time,, for a particular supplier of men’s apparel, the purchasing department of a national department store chain randomly sampled 50 of the supplier’s lead times and found= 44 days.

  1. Describe the shape of the sampling distribution ofx¯.
  2. If μand σare really 40 and 12, respectively, what is the probability that a second random sample of size 50 would yieldx¯ greater than or equal to 44?
  3. Using the values forμ and σin part b, what is the probability that a sample of size 50 would yield a sample mean within the interval μ±2σn?
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