Question

In a large restaurant an average of 3 out of every 5 customers ask for water with their meal. A random sample of 10 customers is selected. Find the probability that Exactly 6 ask for water with their meal and Less than 9 ask for water with their meal

Answer 1

Binomial distribution.

P(=6)

$\binom{10}{6}(\frac{3}{5})^6(\frac{2}{5})^4=0.250823$

p(<9)

$P(<9)=1-P(=9)-P(=10)$

$=1-\binom{10}{9}(\frac{3}{5})^9\frac{2}{5}-(\frac{3}{5})^{10}$

$=1-0.040311-0.06047=0.953643$