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Vera_Pavlovna [14]
3 years ago
6

President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests pe

rformed on a sample of 100 batteries indicated:
(1) an average life of 75 months,
(2) a standard deviation of 5 months,
(3) a bell shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use?
Mathematics
1 answer:
never [62]3 years ago
3 0

Answer:

2.28 %

Step-by-step explanation:

It is stated that battery life distribution is normal. First we need to find out where 65 hour battery life in this distribution falls by finding its z-score. We can use the following formula

z(x)=\frac{X-M}{s}  where

  • X the point we are looking to find its z-score, which is 65
  • M is the mean of the sample, which is 75
  • s is the standard deviation of the sample, which is 5

Replacing these numbers in the formula, z-score of the 65 hour battery life :

z(x)=\frac{65-75}{5}=-2

All the batteries fail within the first 65 months if their z-score is smaller than -2. Or we can state this also as: P(z≤-2) which is 0.0228

Thus 2.28 % of the batteries will fail within the first 65 months of use.

You might be interested in
Can help me find area and perimeter step by step
Vera_Pavlovna [14]

Answer:

  • area: 16.28 ft²
  • perimeter: 17.05 ft

Step-by-step explanation:

The figure is shown as being composed of a semicircle and a triangle. You know the formula for the area of a circle is ...

  A = πr²

The radius of the semicircle is half its diameter, so is (4 ft)/2 = 2 ft. Then the area of a circle with radius 2 feet is ...

  A = π(2 ft)² = 4π ft²

Our semicircle has half that area, so ...

  area of semicircle = (4π ft²)/2 = 2π ft² ≈ 6.283 ft²

__

The area of the triangle is given by the formula ...

  A = (1/2)bh

Here, the base is shown as 4 ft, and the height is shown as 5 ft. Then the triangle area is ...

  triangle area = (1/2)(4 ft)(5 ft) = 10 ft²

So, the total area of the composite figure is ...

  figure area = area of semicircle + triangle area

  = 6.283 ft² + 10 ft² ≈ 16.283 ft² . . . . area of the figure

__

The perimeter of the curved portion of the semicircle is half the circumference of a circle of radius 2 ft. It will be ...

  curved perimeter = (1/2)(2πr) = πr = π(2 ft) = 2π ft ≈ 6.283 ft

The length of each side of the triangle can be found from the Pythagorean theorem. Each side of the triangle is the hypotenuse of a right triangle with legs 2 ft and 5 ft. Then it will be ...

   triangle side length = √(2² +5²) ft = √29 ft ≈ 5.385 ft

The total perimeter is ...

   perimeter = 2 × triangle side length + semicircle length

  = 2×(5.385 ft) + 6.283 ft = 17.054 ft

The perimeter of the figure is about 17.05 feet.

4 0
3 years ago
In math class the girl to boy ratio is 8 to 6 if there are 24 girls in the class , how many boys are there ?
Volgvan

Answer:  The required number of boys in the class is 18.

Step-by-step explanation: Given that in math class, the girl to boy ratio is 8 to 6 and there are 24 girls in the class.

We are to find the number of boys in the class.

Let 8x and 6x represents the number of girls and boys in the class.

Then, according to the given information, we have

8x=24\\\\\Rightarrow x=\dfrac{24}{8}\\\\\Rightarrow x=3.

Therefore, the number of boys in the class is given by

6x=6\times3=18.

Thus, the required number of boys in the class is 18.

7 0
3 years ago
Kedwin has $150 and wants to buy a new pair of headphones that cost $175 + 10% shipping he decides wait until the headphones guy
SOVA2 [1]

Answer:

23%

Step-by-step explanation:

175 x 0.23 = 40.25

175-40.25 = 134.75

134.75 x 10% shipping = 13.48

134.75+13.48=148.23

7 0
3 years ago
How to solve this substitution​
Lena [83]
-5x+4y=11
substitute for x which is 5
(-5)(5)+4y=11

simplify :
4y-25=11

add 25 on both sides
4y-25=11
+25 +25
the 25 cancels out

so it would be 4y=36
and you divide both sides by 4

4/4 =36/4

which gives you (5,9)
x= 5 , y =9
6 0
3 years ago
8.9 - (-2 x 2.4 ) + 3
quester [9]
Use a calculator it’s easier and will give u an instant answer
6 0
3 years ago
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