Before a computer is assembled, its motherboard goes through a special inspection. Assume only 85% of motherboards pass this inspection.

(a) What is the probability that at least 13 of the next 15 motherboards pass inspection?
(b) On the average, how many motherboards should be inspected until a motherboard that passes inspection is found?

(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,

(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)

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:

Thus, on average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.

answer: 10 meter

step-by-step explanation:

need details

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.