Multiply using an area model (5a) (3a

2. The quality assurance department inspects its production line. The product either fails or passes the inspection. Past experi

Oksana_A [137]

Answer:

(a) $E(X) = 950$

(b) $COV = 0.007255$

(c) $P(X > 980) = 0.00001\\\\$

Step-by-step explanation:

The given problem can be solved using binomial distribution since the product either fails or passes, the probability of failure or success is fixed and there are n repeated trials.

probability of failure = q = 0.05

probability of success = p = 1 - 0.05 = 0.95

number of trials = n = 1000

(a) What is the expected number of non-defective units?

The expected number of non-defective units is given by

$E(X) = n \times p \\\\E(X) = 1000 \times 0.95 \\\\E(X) = 950$

(b) what is the COV of the number of non-defective units?

The coefficient of variance is given by

$COV = \frac{\sigma}{E(X)}$

Where the standard deviation is given by

$\sigma = \sqrt{n \times p\times q} \\\\\sigma = \sqrt{1000 \times 0.95\times 0.05} \\\\\sigma = 6.892$

So the coefficient of variance is

$COV = \frac{6.892}{950}$

$COV = 0.007255$

(c) What is the probability of having more than 980 non-defective units?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and so is p.

$P(X > 980) = 1 - P(X < 980)\\\\P(X > 980) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\$

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).

$P(X > 980) = 1 - P(Z < \frac{979.5 - 950}{6.892} )\\\\P(X > 980) = 1 - P(Z < \frac{29.5}{6.892} )\\\\P(X > 980) = 1 - P(Z < 4.28)\\\\$

The z-score corresponding to 4.28 is 0.99999

$P(X > 980) = 1 - 0.99999\\\\P(X > 980) = 0.00001\\\\$

So it means that it is very unlikely that there will be more than 980 non-defective units.

8 0

4 years ago

List all the factors of the composite number 146

4vir4ik [10]

Factors: 1, 2, 73, 146.

4 0

3 years ago

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Mr. Evans is paid $9. 20 per hour for the first 40 hours he works in a week. He is paid 1. 5 times that rate for each hour after

Dmitry_Shevchenko [17]

No, he almost earns $400
9.20 / 1.5 = 6.13
9.20 - 6.13 = 3.07
9.20 + 3.07 = 12.27
12.27 x 2.25 = 27.61
9.20 x 40 = 368
368 + 27.61 = 395.61
Mr. Evans earned $395.61 for 42.25 hrs.

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3 years ago

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1. -168 < -12a

kotegsom [21]

Answer:

See step by step explanation

Step-by-step explanation:

1. a<14

2. m </ 25

3. n >/ 7

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3 years ago

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Select the correct answer. The function g(x) = x2 is transformed to obtain function h: h(x) = g(x) − 5. Which statement describe

crimeas [40]

The graph of h(x) is the graph of g vertically shifted down 5 units. Then the correct option is C.

<h3>What is a function?</h3>

Functions are found all across mathematics and are required for the creation of complex relationships.

The function g(x) = x² is transformed to obtain function h:

h(x) = g(x) − 5

h(x) = x² − 5

The graph h(x) get shifted downward by 5 units.

Then the correct option is C.

More about the function link is given below.

brainly.com/question/5245372

#SPJ1

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2 years ago

Multiply using an area model (5a) (3a - 4)