Answer to Question #188808 in Statistics and Probability for Jessica

Question

 In Pleasantville about 25% of the residents prefer vanilla ice cream over other flavors. A certain day, 175 residents of Pleasantville went to an ice cream store, what is the probabil- ity that 50 or more will get vanilla ice cream?

Answer 1

p = 0.25

q = 0.75

n = 175

Using binomial distribution:

Mean:

$\mu = n \times p = 175 \times 0.25 = 43.75$

Standard deviation:

$\sigma = \sqrt{n \times p \times q} = \sqrt{175 \times 0.25 \times 0.75} = 5.728$

$P(X≥50) = 1 -P(X<49.5) \\ = 1 -P(Z< \frac{49.5 -43.75}{5.728}) \\ = 1 -P(Z<0.197) \\ = 1 -0.5780 \\ = 0.422$