In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 158. What is the probability that the sample proportion will be at least 3 percent more than the population proportion?

The probability that the sample proportion will be at least 3 percent more than the population proportion is 0.6157

Step-by-step explanation:

We need sample proportion between 0.75 - 0.03 = 0.72 and 0.75 +0.03 = 0.78. Here we have p = 0.75 and n= 158.

So z-score for sample proportion q = 0.72

z = = = - = - 0.872

So z-score for sample proportion q = 0.78

z= = =   = 0.872

Therefore the probability that the sample proportion will be within 3 percent of the population proportion is

P( 0.72 < q < 0.78) = P ( -0.872 < z < 0.872)

= P( z < 0.872) - P( z < -0.872)

= 0.80785 - 0.19215

= 0.6157

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for