Respuesta :
Answer:
(a) The probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b) On average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.
Step-by-step explanation:
Let X = number of motherboards that pass the inspection.
The probability that a motherboards pass the inspection is P (X) = p = 0.85.
The random variable X follows a Binomial distribution with parameters n and p.
The probability mass function of X is,
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...[/tex]
(a)
Compute the probability that at least 13 of the next 15 motherboards pass inspection as follows:
P (X ≥ 13) = P (X= 13) + P (X = 14) + P (x = 15)
[tex]={15\choose 13}0.85^{13}(1-0.85)^{15-13}+{15\choose 13}0.85^{14}(1-0.85)^{15-14}\\+{15\choose 13}0.85^{16}(1-0.85)^{15-15}\\=0.2856+0.2312+0.0874\\=0.6042[/tex]
Thus, the probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b)
Computed the expected number of motherboards should be inspected until a motherboard that passes inspection is found as follows:
[tex]Expected\ value=\frac{1}{p}=\frac{1}{0.85}= 1.1764\approx1.18[/tex]
Thus, on average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.
