John Wiley & Sons TI-83 User Manual download pdf (Page 48)

Probabilities for Sample Proportions

For a large sample size, we know from the Central Limit Theorem that the sampling distribution

for ê is normally distributed with µ

= p and σ

npq/

To find the probability that a < ê < b on the calculator, use normalcdf(a, b, p,

npq/

). Note

that it is more accurate to type

npq/

directly into the normalcdf( command than to compute it

separately and type it in. Any time you find yourself typing in an intermediate result in a

computation you may be performing some unnecessary rounding.

Example: Good Times Ahead

According to a 2002 University of Michigan survey, about one-third of Americans are expecting

the next five years to bring continuous good times. Assume that 33% of all Americans hold this

opinion. If 800 Americans are randomly selected and polled, what is the likelihood that between

35% and 37% of the sample will have this opinion?

Select normalcdf( from the DISTR list.

Type in 0.35, 0.37, 0.33,

800/67.*33.)

Press the ENTER key.

The probability is .106 or 10.6%

Example: Voters

A candidate for mayor in a large city claims that she is favored by 53% of all eligible voters of

that city. Assume that the claim is true. What is the probability that in a random sample of 400

registered voters taken from this city, less than 49% will favor the candidate?

normalcdf(−1E99, 0.49, 0.53,

400/47.*53. ) = 0.0545 = 5.45%.

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John Wiley & Sons TI-83 User Manual Page 48