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Gnesinka [82]
3 years ago
14

Suppose I work on a factory line doing quality control work. Since I've been working here for such a long time, I am fairly conf

ident that 15% of all items (independent of all other items) need to be sent back to be re-worked. These items take a fairly long time to check properly, but it is the same set of steps every time, so I always check 25 items every shift. Let X be the number of items sent back to be re-worked during a given shift. What is the distribution of X? Give the name of the distribution and the appropriate parameters. What is the mean and variance of this distribution? Give your answer as a number, but include the formulas (or logic) used. What is the probability I send back less than 4 items to be re-worked during a single shift? What is the probability I send back exactly 3 items to be re-worked during a single shift?
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
8 0

Answer:

Step-by-step explanation:

a) It is a binomial distribution.

n = 25

p = 0.15

b) mean = np = 25 * 0.15 = 3.75

   variance = np(1 - p)

                 = 25 * 0.15 * (1 - 0.15)

                 = 3.1875

c) P(X = x) = nCx * px * (1 - p)n - x

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

            = 25C0 * (0.15)^0 * (0.85)^25 + 25C1 * (0.15)^1 * (0.85)^24 + 25C2 * (0.15)^2 * (0.85)^23 + 25C3 * (0.15)^3 * (0.85)^22 = 0.4711

d) P(X = 3) = 25C3 * (0.15)^3 * (0.85)^22 = 0.2174

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x = None

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Step-by-step explanation:

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3 years ago
Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years af
Leno4ka [110]

The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

<h3>What is compound interest?</h3>

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate<em> r </em>of in the time period of <em>t.</em>

Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.

Put the values in the above formula as,

5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29

In the 10 years, the refund she gets,

A_r=63.29\times12\times100\\A_r=7594.8

Interest paid by her is,

I=7594.8-5500\\I=2094.8

Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

Learn more about the compound interest here;

brainly.com/question/24274034

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2 years ago
Please help me answer this question
fredd [130]

Answer:

2t + 16

Step-by-step explanation:

1. 0 seconds and 16 feet.

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2. 1 second and 18 feet.

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  • 2 + 16
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3. 2 seconds and 20 feet.

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4. 3 seconds and 22 feet.

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5. 6 seconds and 28 feet.

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Therefore, the answer is 2t + 16.

4 0
2 years ago
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