Question

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed. 139<x<148

Find the indicated probability using the standard normal distribution.

P(−1.65<z<1.65)

As part of your work for an environmental awareness group, you want to test the claim that the mean waste generated by adults in the country is more than

55

pounds per person per day. In a random sample of

99

adults in the country, you find that the mean waste generated per person per day is

5.85.8

pounds and the standard deviation is

1.91.9

pounds. At

alpha equals 0.05α=0.05 ,

can you support the claim? Assume the population is normally distributed.

(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

b) Find the critical value(s) and identify the rejection region(s).

What is(are) the critical value(s),

t 0t0 ?

t 0t0equals=nothing

38% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.

In a survey of

613613

males ages 18-64,

399399

say they have gone to the dentist in the past year.

Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval for the population proportion p is

(nothing ,nothing ).

(Round to three decimal places as needed.)

The 95% confidence interval for the population proportion p is

(nothing ,nothing ).

(Round to three decimal places as needed.)

Interpret your results of both confidence intervals.

A.

With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

B.

With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

C.

With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.

Answer 1

1. P(−1.65<z<1.65)=P(Z<1.65)-P(Z<-1.65)=0.9505-0.0495=0.9011

2. (a) The null and alternative hypothesis is

  

  

(b) Given that α=0.05 and n=99. the critical value for a right-tailed test is t0 = 1.661.

The rejection region for this right-tailed test is R = {t: t > 1.661}.

3. Given that p=0.38 and n=12,

Here X:the number od adults who said cashews are their favorite nut.

X~Binomial(12,0.38)

	Notation	Excel Function	Probabilities
Exactly Three	P(X=3)	Binomdist(3,12,0.38,false	0.1634
At least Four	P(X>=4)	1-Binomdist(3,12,0.38,True)	0.7296
At most Two	P(X<=2)	Binomdist(2,12,0.38,True	0.1069

3. Given that X=399399 and n=613613

  

The 90% confidence interval for the population proportion p is (0.65,0.652)

The 95% confidence interval for the population proportion p is (0.65,0.652)

Interpetation:

B.

With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.