Answer to Question #182488 in Statistics and Probability for Carol

Question

1.     You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands.

 

REQUIRED:

a)        What is the probability that the sample will have between 50% and 60% of the identifications correct?

Answer 1

population proportion p=0.5

n=200

standard error of $\hat{p}=\sqrt{\dfrac{0.5*(1-0.5)}{200}}=0.0354$

a)

$z(0.5)=0$

$z(0.60)=\dfrac{(0.60-0.50)}{0.0354}=2.82$

$P(0<z<2.82)=P(z<2.82)-P(z<0)$

$=0.9976-0.5=0.4976$