Mathematics
The Sample Proportion

Question Description

Final Answer

Sample size n is 450.

Standard deviation of a proportion p is given by sqrt(p(1-p))

sd = sqrt(0.07 x 0.93)

= 0.255

So the standard error for a sample mean is given by sd/sqrt(n) where n is the sample size:

SEM = sd/sqrt(n)

= 0.255/sqrt(450)

= 0.012

25/450 and 35/450 are 0.055555556 and 0.077777778. The probability our mean will lie between these will be given by the cdf at 0.0777778, minus the cdf at 0.0555556 (consider what the cdf means: The area under the curve to the left of that point).

So the probability that fewer than 25-25 will have no home phone in our sample of 450 is the normal cdf at .0777778 with mean = .07 and sd = SEM = 0.012 minus the normal cdf at .0555556 with mean = .07 and sd = SEM = 0.012:

= Norm.cdf (0.078, 0.07, 0.012) - Norm.cdf (0.056, 0.07, 0.012)

0.741071724 - 0.114889762

= 0.626



iainharlow (1041)
Duke University

Anonymous
I was on a very tight deadline but thanks to Studypool I was able to deliver my assignment on time.

Anonymous
The tutor was pretty knowledgeable, efficient and polite. Great service!

Anonymous
I did not know how to approach this question, Studypool helped me a lot.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4
Similar Questions
Related Tags

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors