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Lerok [7]
3 years ago
14

The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviat

ion of 2 months. Find the probability that an instrument produced by this machine will last Q.1. Between 7 and 12 months. Q.2. . Less than 7 months Q.3. More than 5 months but less than 10 months

Mathematics
2 answers:
Minchanka [31]3 years ago
7 0

Answer:

Q.1. 0.4938

Q.2. 0.0062

Q.3. 0.1587

Step-by-step explanation:

Data

  • mean, μ = 12
  • standard deviation, σ = 2

In the figure attached, the standard normal distribution table is shown.

Z = (x - μ)/σ

Q.1.

if x = 7, then Z = (7 - 12)/2 = -2.5

if x = 12, then Z = (12 - 12)/2 = 0

We want to find:

P(-2.5 < Z < 0) = P(Z < 0) - P(Z < -2.5) = 0.5 - 0.0062 = 0.4938

Q.2.

We want to find:

P(Z < -2.5) = 0.0062

Q.3.

if x = 5, then Z = (5 - 12)/2 = -3.5

if x = 10, then Z = (10 - 12)/2 = -1

We want to find:

P(-3.5 < Z < -1) = P(Z < -1) - P(Z < -3.5) = 0.1587 - 0 = 0.1587

Vikentia [17]3 years ago
6 0

Answer:

solved

Step-by-step explanation:

Mean = 12

SD = 2

Answer to part 2)  Less than 7 months

P(x < 7)

P(x < 7) = P(z < (7-12)/2) = P(z < -2.5)

This probability can be obtained by referring to the Z table

Thus P(x < 7) = 0.0062

1) Between 7 and 12 months

P(7 < x < 12) = P( x< 12) - P(x < 7)

We have P(x < 12) = 0 ......[because mean = 12]

and P(x < 7) = 0.0062 ...[this we got is part a]

Thus on plugging these values we get

P( 7 < x < 12) = 0.5 - 0.0062 = 0.4938

Thus P(7 < x < 12) = 0.4938

3

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-x²+x+20     | x+4
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The graph is a decreasing line, with origin from 5.



   

3 0
3 years ago
Mr. O'Connor had $90 to spend at a football game. He spent 31/45 on his ticket. Then, he spent 3/7 of his remaining money at the
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4 0
3 years ago
Evaluate 0.3 y+\dfrac yz0.3y+ z y ​ 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals,
sergij07 [2.7K]

Answer:

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Step-by-step explanation:

Put the numbers where the corresponding variables are in the formula and do the arithmetic.

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The expression evaluates to 5.

6 0
3 years ago
In parallelogram JKLM, m&lt;L exceeds m&lt;M by 30 degrees. What is the measure of M&lt;J?
Damm [24]

 

Answer:

2)105°

Step-by-step explanation:

In this parallelogram, J should be congruent to L (J=L). We can solve this problem if we find out the value of L.

The sum of the adjacent angle of the parallelogram will be equal to 180 degrees, so  the equation is

L + M = 180

M=180- L

If L exceeds M by 30 degrees then the equation will be

L=M +30  

If you combine both equations, it will be

L+30 = M +30

L+30 = (180- L) +30

L + L= 180 + 30

2L= 210

L=105

3 0
3 years ago
Why the order of the coordinates does not matter when calculating length
Rudiy27
The formula for calculating length is:
\sqrt{ (x_b-x_a)^{2} + (y_b-y_a)^{2} }

We can also write x_a - x_b or y_a - y_b
Why it does not matter?
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When we perform a subtraction:
a-b, we get another number c
When we perform another subtraction:
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When we raise c or -c to the power of 2, the result is the same, c^{2}.
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