1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viktor [21]
3 years ago
15

A company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car doe

s not change. Suppose that only 20% of its mufflers are replaced under this warranty.a. In a random sample of 400 purchases, what is the approximate probability that between 75 and 100 (inclusive) mufflers are replaced under warranty?b. Among 400 randomly selected purchases, what is the probability that at most 70 mufflers are ultimately replaced under warranty?c. If you were told that fewer than 50 among 400 randomly selected purchases were ever replaced under warranty, would you question the 20% figure? Explain.
Mathematics
1 answer:
zubka84 [21]3 years ago
7 0

Answer:

a) 0.728

b) 0.106

c) Yes,

The mean given needs to be seriously questioned because, for a normal distribution, all of the possible values (95% of the values) should lie within the range of z = -3 and z = 3. The value for z = - 3.75 is an outlier and shouldn't happen for a normal distribution.

Step-by-step explanation:

Mean = xbar = np = 400 × 0.2 = 80

Standard deviation = √[np(1-p)] = √(80×0.8) = 8

Condition for the distribution to be a normal distribution

np ≥ 10

80 ≥ 10

And

np(1-p) ≥ 10

80(0.8) = 320 ≥ 10

Hence, we use the z-tables for this

a) The approximate probability that between 75 and 100 (inclusive) mufflers are replaced under warranty?

We convert the values 75 and 100 to standardized scores.

The standardized score for a value is the value minus the mean then divided by the standard deviation.

z = (x - xbar)/σ

For 75

z = (75 - 80)/8 = - 0.625

For 100

z = (100 - 80)/8 = 2.5

To find the approximate probability that between 75 and 100 (inclusive) mufflers are replaced under warranty

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)

We'll use data from the normal probability table for these probabilities

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5) = P(z ≤ 2.5) - P(z ≤ -0.625) = 0.994 - 0.266 = 0.728

b) Among 400 randomly selected purchases, what is the probability that at most 70 mufflers are ultimately replaced under warranty?

We convert the value 7 to standardized scores.

z = (x - xbar)/σ = (70 - 80)/8 = - 1.25

To find the approximate probability that at most 70 mufflers are replaced under warranty

P(x ≤ 70) = P(z ≤ -1.25)

We'll use data from the normal probability table for these probabilities

P(x ≤ 70) = P(z ≤ -1.25) = 0.106

c) If you were told that fewer than 50 among 400 randomly selected purchases were ever replaced under warranty, would you question the 20% figure? Explain.

We first convert 50 to standard scores

z = (x - xbar)/σ = (50 - 80)/8 = - 3.75

The mean given needs to be seriously questioned then, because for a normal distribution, all of the possible values (95%) should lie within the range of z = -3 and z = 3. The value for z = - 3.75 is an outlier for normal distribution.

You might be interested in
What is Three-Quarters of Three-Quarters?
madam [21]
3/4 * 3/4


Three quarter meaning 3/4
Of represents *
So the answers is (3*3)/(4*4)=9/16 or 0.5625
8 0
3 years ago
Helpppppppppppppppppppppppppppppp
3241004551 [841]
Answer:

first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.

Explanation:

1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.

2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4

3) sin (π/4) = sin (3π/4) = (√2) / 2

4) csc (π/4) =  1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.
3 0
3 years ago
Which ordered pair is a solution to the equation y=-2x+10
wolverine [178]
Are there any answer choices?
7 0
3 years ago
Read 2 more answers
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
devlian [24]

Answer:

The rocket will reach its maximum height after 6.13 seconds

Step-by-step explanation:

To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height

∵ y is the height of the rocket after launch, x seconds

∵ y = -16x² + 196x + 126

- Differentiate y with respect to x

∴ y' = -16(2)x + 196

∴ y' = -32x + 196

- Equate y' by 0

∴ 0 = -32x + 196

- Add 32x to both sides

∴ 32x = 196

- Divide both sides by 32

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

∴ The rocket will reach its maximum height after 6.13 seconds

There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h = -\frac{b}{2a} and k is the value of y at x = h and k is the maximum/minimum value

∵ a = -16 , b = 196

∴ h=-\frac{196}{2(-16)}

∴ h = 6.125

∵ h is the value of x at the maximum height

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

4 0
3 years ago
Phil ran 4 3/8 miles yesterday. Michael ran 1 5/8 miles yesterday. How much farther did phil run than Michael
djyliett [7]
Phil ran 2 7/8 miles more than micheal
8 0
2 years ago
Other questions:
  • The circumference of a circle that has a radius of 7cm. use 3.14. for pie
    13·1 answer
  • PLEASE HELP THIS IS THE LAST QUESTION AND I WANT TO GO TO BED. PLEASE EXPLAIN SO I CAN DO IT FOR NEXT TIME AS WELL
    13·1 answer
  • Two workers can make two chairs in two days. How many chairs can 8 workers working at the same rate make in 20 days?
    13·1 answer
  • Bella is 161 Centimeters tall. She is 12 centimeters taller than Joshua, How tall is Joshua?
    14·2 answers
  • A basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet,
    10·1 answer
  • What is the diameter and radius also the area
    5·1 answer
  • Help help help helphelp​
    11·1 answer
  • Help! no links please and thank you
    6·1 answer
  • Emily, Zeke, Harry, and Brook each conducted surveys on the number of books people have in their homes. Then, each student deter
    6·2 answers
  • Ateacher records the number of students present in her 1st period class each day
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!