compute probability using binomial distribution

Question

Question: Of the customers purchasing laptops, 75% purchase a Dell model. Let X = number among the next 15 purchasers who select the Dell model. (a) Compute P(X>10), b) Compute P(6<= X <=10). Is a) the same as P(X = 10) ? and would someone please set up the conditional for b) ? Thanks!!

Answer 1

P(X>10)=.6865 P(6<= X <=10)=.3127 P(X = 10)=.1651

I am not sure what you mean by the conditional for b.

Answer 2

$n=15$, $p=0.75$, $q=0.25$.

$P(X=10)=C_{15}^{10} 0.75^{10}0.25^5$

$P(X >10)=\sum_{i=11}^{15} C_{15}^{i} 0.75^{i}0.25^{15-i}$

$P(6\le X\le 10)=\sum_{i=6}^{10} C_{15}^{i} 0.75^{i}0.25^{15-i}$