### 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

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