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Chapter 4: Q119E (page 268)

Normal probability plots for three data sets are shown on the next page. Which plot indicates that the data are approximately normally distributed?

Short Answer

Expert verified

The plot in part-(c) indicates that data is normally distributed.

Step by step solution

01

Given Information

02

Explanation

In the first plot (i.e,part-(a))if we draw a straight line then maximum data points fall below the straight line, so the data is not normally distributed.

In the second plot (i.e,part-(b))if we draw a straight line then maximum data points fall above the straight line, so the data is not normally distributed.

In the third plot (i.e, part-(c) if we draw a straight line then maximum data points fall on the straight line, so the data is normally distributed.

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Most popular questions from this chapter

Ambulance response time. Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance. Geographical Analysis (Vol. 41, 2009) investigated the characteristics of ambulance response time for EMS calls in Edmonton, Alberta. For a particular EMS station (call it Station A), ambulance response time is known to be normally distributed with m = 7.5 minutes and s = 2.5 minutes.

a. Regulations require that 90% of all emergency calls be reached in 9 minutes or less. Are the regulations met at EMS Station A? Explain.

b. A randomly selected EMS call in Edmonton has an ambulance response time of 2 minutes. Is it likely that this call was serviced by Station A? Explain

Box plots and the standard normal distribution. What relationship exists between the standard normal distribution and the box-plot methodology (Section 2.8) for describing distributions of data using quartiles? The answer depends on the true underlying probability distribution of the data. Assume for the remainder of this exercise that the distribution is normal.

a. Calculate the values of the standard normal random variable z, call them zL and zU, that correspond to the hinges of the box plot鈥攖hat is, the lower and upper quartiles, QL and QU鈥攐f the probability distribution.

b. Calculate the zvalues that correspond to the inner fences of the box plot for a normal probability distribution.

c. Calculate the zvalues that correspond to the outer fences of the box plot for a normal probability distribution.

d. What is the probability that observation lies beyond the inner fences of a normal probability distribution? The outer fences?

e. Can you better understand why the inner and outer fences of a box plot are used to detect outliers in a distribution? Explain.

Explain why each of the following is or is not a valid probability distribution for a discrete random variable x:

a.

x0123
P(x).1.3.3.2

b.

x-2-10
P(x).25.50.25

c.

x4920
P(x)-3.4.3

d.

x2356
P(x).15.15.45.35

Find each of the following probabilities for the standard normal random variable z:

a.P(-鈮�z鈮�1)b.P(-1.96鈮�z鈮�1.96)c.P(-1645鈮�z鈮�1.645)d.P(-2鈮�z鈮�2)

Find a value of the standard normal random variable z, call itz0 such that

a.P(-z0鈮�z鈮�z0)=.98b.P(z鈮�z0)=.05c.P(z鈮�z0)=.70d.P(z鈮�z0)=.025e.P(z鈮�z0)=.70
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