A robot can complete 8 tasks in 3/4 hour. Each task takes the same amount of time.

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

Silvia was growing some plants. She measured the height, in inches, of the plants and made thisline plot to show her data:

FromTheMoon [43]

Answer:

The answer is C.

Step-by-step explanation:

The equivalents to 1/4 are 2/8, 3/12, 4/16 etc. So the fractions after 1/4 are higher than 1/4. Then you count how many 'x's are in the columns for those measurements and you will get 6.

5 0

3 years ago

What is the number 0.000706 written in scientific notation?

Alex17521 [72]

Answer:

7.6 x 10^-4

Step-by-step explanation:

5 0

3 years ago

The curve with equation y2 = x3 + 3x2 is called the tschirnhausen cubic. find an equation of the tangent line to this curve at t

MAVERICK [17]

First find the slope, take derivative of both sides with respect to x.
2y dy/dx=3x^2+6x
solve for dy/dx
dy/dx=[3x^2+6x]/2y
plug in given vales of (1,2(
dy/dx=9/4

now you have everything you need to plug into point slope form
y-2=(9/4)(x-1)
answer is y=(9/4)x+(1/4)

5 0

3 years ago

A jacket that cost a store $120 was marked up to $168. What percent was the mark up?

german

Answer:

48%

Step-by-step explanation:

you have to subtract 168 and 120

8 0

3 years ago

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