A popular toothpaste brand claims that four out of five (or eighty percent) of dentists recommend...

A popular toothpaste brand claims that four out of five (or eighty percent) of dentists recommend their brand.

1. You randomly select 35 dentists. Calculate the probability that the sample proportion is between 74 percent and 88 percent.

2. Comment on the appropriateness of the sample size.

Expert Solution

1)

Sample size , n =    35
Probability of an event of interest, p =   0.80
we need to calculate probability for ,
25.9   ≤ X ≤    30.8
Mean = np =    28
std dev ,σ=√np(1-p)=   2.3664

P (   25.9   ≤ X ≤    30.8   )
Z1 =   (X1 - µ ) / σ =   -0.887
Z2 =   (X2- µ ) / σ =   1.183

P (    -0.8874   ≤ Z ≤   1.183   )

= P ( Z ≤   1.183   ) - P ( Z ≤   -0.887   ) =    0.8816   -    0.1874   =   0.6942

2)

Sample size is greater than 30. Also mean is high and that's why we have used normal approximation to calculate above probability.

THANKS

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orchestra answered 2 years ago

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