Question

Up to 20% of Americans contract influenza each year. A sample of 400 randomly selected Americans is chosen and the number with influenza is recorded. Let X represent the number with influenza in the sample. What is the probability that, at most, 25% of the sample is observed to have influenza? How can I do this the easiest way on Ti-84? Can I use a button like Stats or Distr to make life easy?

Answer 1

The probability can be calculated by using Z statistics.

Formula:

Here,

P₀ = 0.2 (20% is the proportion for the population)

P = 0.25

So,

Z = (0.25 - 0.2)/{0.2(1 - 0.2)/400}^0.5

So, Z = 2.5

So, the corresponding probability for Z = 2.5 is 0.9938

So, there is a probability of 0.9938 that, at most, 25% of the sample is observed to have influenza.

Refer the Z table for more clarity...

In Ti-84, you can use functions for z statistics to get the desired result.

End of the Solution...