Question

according to the federal communications commission, 70% of all u.s. households have dvd players. in a random sample of 15 households, what is the probability that the number of households with dvd players is between 10 and 12, inclusive? round to four decimal places.

a. 0.2061
b. 0.5948
c. 0.7
d. 0.4053

Explanation:

Step1: Identify the binomial probability formula

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n = 15\), \(p=0.7\), \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Calculate \(P(X = 10)\)

$$
LATEXBLOCK0
$$

Step3: Calculate \(P(X = 11)\)

$$
LATEXBLOCK1
$$

Step4: Calculate \(P(X = 12)\)

$$
LATEXBLOCK2
$$

Step5: Calculate \(P(10\leq X\leq12)\)

\(P(10\leq X\leq12)=P(X = 10)+P(X = 11)+P(X = 12)=0.2061 + 0.2187+0.1700 = 0.5948\)

Answer:

B. 0.5948