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Nataly_w [17]
2 years ago
7

(a) A lamp has two bulbs, each of a type with average lifetime 1400 hours. Assuming that we can model the probability of failure

of these bulbs by an exponential density function with mean μ = 1400, find the probability that both of the lamp's bulbs fail within 1700 hours. (Round your answer to four decimal places.)
Mathematics
1 answer:
Temka [501]2 years ago
8 0

Answer:

For first lamp ; The resultant probability is 0.703

For both lamps; The resultant probability is 0.3614

Step-by-step explanation:

Let X be the lifetime hours of two bulbs

X∼exp(1/1400)

f(x)=1/1400e−1/1400x

P(X<x)=1−e−1/1400x

X∼exp⁡(1/1400)

f(x)=1/1400 e−1/1400x

P(X<x)=1−e−1/1400x

The probability that both of the lamp bulbs fail within 1700 hours is calculated below,

P(X≤1700)=1−e−1/1400×1700

=1−e−1.21=0.703

The resultant probability is 0.703

Let Y be a lifetime of another lamp two bulbs

Then the Z = X + Y will follow gamma distribution that is,

X+Y=Z∼gamma(2,1/1400)

2λZ∼

X+Y=Z∼gamma(2,1/1400)

2λZ∼χ2α2

The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,

P(Z≤1700)=P(1/700Z≤1.67)=

P(χ24≤1.67)=0.3614

The resultant probability is 0.3614

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Step-by-step explanation:

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3 0
3 years ago
elise takes 12 minutes to rake up and bag a pile of leaves her sister katherine takes twice as long, how many minutes would it t
Ymorist [56]

Answer:

80 minutes

Step-by-step explanation:

Rate and Time are inverses of each other

First,

Elise Time = 12

and

Katherine Time = 2 * 12 = 24

Their rates would be (inverses):

Elise Rate = 1/12

Katherine Rate = 1/24

Together their rate is 1/12 + 1/24 = 3/24

Now, the inverse of this rate would be the time it takes to complete 1 bag together, that is:

(3/24) ^ -1 = 24/3 = 8 minutes

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8 0
3 years ago
What is the mean for the data set?
PIT_PIT [208]
83.3
Just add up all the numbers and divide by 6, as there are six numbers in this set of numbers
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Read 2 more answers
Solve for x in the equation 2x^2-4x-9=29
Andrews [41]

Answer:

x = 1  ±2sqrt(5)

Step-by-step explanation:

2x^2-4x-9=29

Add 9 to each each side

2x^2-4x-9+9=29+9

2x^2-4x=38

Divide by 2

2/2x^2-4/2x=38/8

x^2 -2x =19

Complete the square

x^2 -2x + (-2/2)^2 = 19 +(-2/2)^2

x^2 -2x +1 = 19+1

(x-1)^1=2 = 20

Take the square root of each side

sqrt((x-1)^2) = ±sqrt(20)

x-1 =  ±sqrt(20)

Add 1 to each side

x-1+1 = 1  ±sqrt(20)

x = 1 ±sqrt(20)

Simplifying the square root of 20

x = 1  ±sqrt(4)sqrt(5)

x = 1  ±2sqrt(5)

3 0
3 years ago
Apple would like to estimate the web browsing battery life of the iPad. The following data represents the battery life, in hours
umka21 [38]

Answer:

12.5 hours

Step-by-step explanation:

The data which represents the battery life, in hours, experienced by six users is given below:

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To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.

Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5

The point estimate for the web browsing battery life of the iPad is: 12.5 hours

8 0
3 years ago
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