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Chapter 12: Q. 8 (page 800)

A large machine is filled with thousands of small

pieces of candy, 40%of which are orange. When money

is deposited, the machine dispenses 60randomly selected

pieces of candy. The machine will be recalibrated if a

group of 60candies contains fewer than18 that are

orange. What is the approximate probability that this will

happen?

a)Pz<0.3-0.4(0.4)(0.6)60

b)Pz<0.4-0.3(0.3)(0.7)60

role="math" localid="1650519113387" c)Pz<0.3-0.4(0.4)(0.6)60

role="math" localid="1650519757907" d)Pz<0.3-0.4(0.4)(0.6)60

e)Pz<0.4-0.3(0.3)(0.7)60

Short Answer

Expert verified

The answer is optiona)Pz<0.3-0.4(0.4)(0.6)60

Step by step solution

01

Given Information

40%of the small candies are orange.

On depositing money, the machine dispenses 60randomly selected pieces of candy.

The machine will be recalibrated if a group of 60candies contains fewer than 18that are orange.

02

Simplification

The problem is about population proportions. The problem states that 40%are orange indicating the true population proportion being 0.4.

The Z score formula for proportions is:

Z=p^-pp脳(1-p)n

18of the 60candies is 30percent. Therefore, the correct boundary when plugging in the number is:

Z=0.3-0.40.4脳0.660

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Most popular questions from this chapter

A distribution of exam scores has mean 60and standard deviation 18. If each score is doubled, and then 5is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores?

(a) mean=115and standard deviation=31

(b) mean=115and standard deviation=36

(c) mean=120and standard deviation=6

(d) mean=120and standard deviation=31

(e) mean=120 and standard deviation=36

The swinging pendulum Refer to Exercise 33. Here is Minitab output from separate regression analyses of the two sets of transformed pendulum data:

Do each of the following for both transformations.

(a) Give the equation of the least-squares regression line. Define any variables you use.

(b) Use the model from part (a) to predict the period of a pendulum with length of 80 centimeters. Show your work.

(c) Interpret the value of s in context

Refer to Exercise 5.

(a) Interpret the value of SEb in context.

(b) Find the critical value for a 90% confidence interval for the slope of the true regression line. Then calculate the confidence interval. Show your work.

(c) Interpret the interval from part (b) in context.

(d) Explain the meaning of 鈥�90% confident鈥� in context.

Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.

The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?

I. Take the square root of the number of Cheerios.

II. Cube the number of Cheerios.

III. Take the log of the number of Cheerios.

IV. Take the log of the diameter.

(a) I and II

(b) I and III

(c) II and III

(d) II and IV

(e) I and IV

In the casting of metal parts, molten metal flows through a 鈥済ate鈥� into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined a random sample of 12 pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process.

Construct and interpret a 95%confidence interval for the slope of the population regression line. Explain how this interval is consistent with the results of Exercise R12.2.
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