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Katen [24]
3 years ago
6

An article in USA Today stated that Internal surveys paid for by directory assistance providers show that even the most accurate

companies give out wrong numbers 15% of the time. Assume that you are testing such a provider by making 10 requests and also assume that the provider gives the wrong telephone number 15% of the time.
Required:
a. Find the probability of getting one wrong number.
b. Find the probability of getting at most one wrong number.
c. If you do get at most one wrong number, does it appear that the rate of wrong numbers is not 15%, as claimed?
Mathematics
1 answer:
MariettaO [177]3 years ago
3 0

Answer:

a. 11.26 % b. 6.76 %. It appears so since 6.76 % ≠ 15 %

Step-by-step explanation:

a. This is a binomial probability.

Let q = probability of giving out wrong number = 15 % = 0.15

p = probability of not giving out wrong number = 1 - q = 1 - 0.15 = 0.75

For a binomial probability, P(x) = ⁿCₓqˣpⁿ⁻ˣ. With n = 10 and x = 1, the probability of getting a number wrong P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹

= 10(0.15)(0.75)⁹

= 1.5(0.0751)

= 0.1126

= 11.26 %

b. At most one wrong is P(x ≤ 1) = P(0) + P(1)

= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹

= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹

= 0.0563 + 0.01126

= 0.06756

= 6.756 %

≅ 6.76 %

Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

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Genrish500 [490]

We need to find two relations, and use them to find the value of y when z = 15.

We will see that the value of y in that case is 4,860.

We know that <u>y  varies inversely with the square of  x</u>, also <u>y  is also proportional to the cube of  z</u>

Then we can write:

y = k/x^2

y = c*z^3

We also know that:

When x = 3, y = 80.

Replacing that in the first equation to find the value of k:

80 = k/3^2

80 = k/9

80*9 = k = 720

We also know that when x = 2, z = 5

From the first relation we have:

y = 720/2^2 = 720/4 = 180

Now we replace this in the equation of y and z:

y = c*z^3

180 = c*5^3

180 = c*125

180/125 = c = 1.44

Now we need to calculate y when z = 15, then we just need to replace z by 15 in the equation for y and z:

y = 1.44*(15)^3 = 4,860.

If you want to learn more, you can read:

brainly.com/question/2548537

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You and a friend are sharing a swing. You have swung 11 times while your friend has swung twice as many times. Which of the foll
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Read 2 more answers
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