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alexandr1967 [171]
3 years ago
10

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.04

flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel. (a) What is the probability that there are no surface flaws in an auto's interior
Mathematics
1 answer:
Furkat [3]3 years ago
4 0

Answer:

(a) Probability that there are no surface flaws in an auto's interior is 0.6703 .

Step-by-step explanation:

We are given that the number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.04 flaws per square foot of plastic panel.

Let X = Distribution of number of surface flaws in plastic panels

So, X ~ Poisson(\lambda)

The mean of Poisson distribution is given by, E(X) = \lambda = 0.04

which means, X ~ Poisson(0.04)

The probability distribution function of a Poisson random variable is:

P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!}; for  x=0,1,2,3...

Now, we know that \lambda for per square foot of plastic panel is 0.04 and we are given that an automobile interior contains 10 square feet of plastic panel.

Therefore, \lambda for 10 square foot of plastic panel is = 10 * 0.04 = 0.4

(a) Probability that there are no surface flaws in an auto's interior =P(X=0)

     P(X = 0) = \frac{e^{-0.4}*0.4^{0}}{0!} = e^{-0.4} = 0.6703

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Black_prince [1.1K]

Answer:

d = 28

r = 14

r² = 196

C = 87.92

Step-by-step explanation:

Given:

r = 14

To find diameter:

d = 2r

d = 2(14)

d = 28

To find r²:

14²

196

Circumference:

C = 2πr

C = 2(3.14)(14)

C = 87.92

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3 years ago
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Tammi deposited $520 into a bank account that earned simple interest each year. After 5 years, she had earned $156 in interest.
topjm [15]

Answer:

6%

Step-by-step explanation:

$156/5 years = $31.20 per year

$31.20/$520 = .06

.06 x 100 = 6%

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3 years ago
HELP ILL GIVE U BRAINLIEST
BaLLatris [955]

Answer:

-6 33/40

Step-by-step explanation:

2\frac{5}{8} = 2.625\\-2\frac{3}{5} = 2.6\\\\2.625 *-2.6 = -6.825\\\\-6.825 = -6\frac{33}{40}

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2 years ago
The area of a triangle with a height of 9 cm and a base of 6 cm is
vazorg [7]

Answer:

27 cm²

Step-by-step explanation:

Formula of Area Triangle = 1/2(base x height)

Base = 6 cm

Height = 9 cm

1/2 ( 6 x 9 ) = 1/2 ( 54 ) = 27

Units = cm * cm = cm²

27 cm²

<u>Why the formula (1/2 ( base x height )) works:</u>

Take a triangle

Duplicate the triangle

And rotate the triangle and put it next to the other one

What shape does it form?

Either a parallelogram or a rectangle

The formula for a parallelogram or rectangle is (base x height)

Since you are initially doubling the area of the triangle to get the rectangle, solve for the rectangle and divide by 2.

So, do base x height

And divide by 2

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2 years ago
) Thirty percent of the students in a management class are graduate students. A random sample of 3 students is selected. a) Usin
skelet666 [1.2K]

Given Information:  

Probability of success = 30%

Sample size = n = 3

Variable of interest = x = 2  

Required Information:  

Probability of exactly 2 graduates = ?

Answer:

Probability of exactly 2 graduates = P(2; 3, 0.30) = 0.189

Step-by-step explanation:

The given problem can be modeled as a binomial experiment since a random selected student can either b graduate or not therefore, there are only 2 outcomes. Each trial is independent and the probability of success is not changing from trial to trial. The number of trials in also fixed.

We know that a binomial distribution is given by

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P(2; 3, 0.30) = 3C2*0.30²*(1 - 0.30)³⁻²

P(2; 3, 0.30) = 3*0.30²*(0.70)¹

P(2; 3, 0.30) = 0.189

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3 years ago
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