Question

Based on internal tests a spaghetti sauce company believes that 70% of people prefer their sauce to the competitor's sauce. They are going to conduct a taste test and want to have a probability of .9 or better that 60% or more of taste testers prefer their product. They are considering groups of taste testers in increments of 10, i.e., 10, 20, 30, 40, ... How many people do they need to participate in the taste test?

Note: Your answer will be divisible by 10 with no remainder.

Answer 1

for n=10:

here this is binomial with parameter n=10 and p=0.7

P(60% or more prefer) =P(X>=6)=1-P(X<=5)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.8497

for n=20:

this is binomial with parameter n=20 and p=0.7

P(60% or more prefer) =P(X>=12)=1-P(X<=11)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.8867

for n=30:

this is binomial with parameter n=30 and p=0.7

P(60% or more prefer) = P(X>=18)=1-P(X<=17)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.9155

since it is higher than 0.9 , therefore correct answer is n= 30