Computers require fans to keep them from overheating. Let T be the random variable representing the lifetime of a particular make of fan in hours. Assume that T follows an exponential distribution with parameter λ = 0.0003. (a) Find the proportion of computer fans which will give at least 10,000 hours of service. (b) If the fan is redesigned so that exponential lifetime distribution now has parameter λ = 0.00035, would you expect more fans or fewer fans to live for at least 10,000 hours?

a) 4.98% of computer fans which will give at least 10,000 hours of service.

b) 3.02% of computer fans which would give at least 10,000 hours of service, that is, fewer fans living for at least 10,000 hours.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

In this problem, we have that:

(a) Find the proportion of computer fans which will give at least 10,000 hours of service.

Either it gives less 10,000 hours of service, or it gives at least 10,000. The sum of the probabilities of these events is decimal 1. So

We want . So

4.98% of computer fans which will give at least 10,000 hours of service.

(b) If the fan is redesigned so that exponential lifetime distribution now has parameter λ = 0.00035, would you expect more fans or fewer fans to live for at least 10,000 hours?

Now

3.02% of computer fans which would give at least 10,000 hours of service, that is, fewer fans living for at least 10,000 hours.

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: