What is the biweekly salary equivalent to a monthly salary of $3434.08

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

the average age of four men is 40. If the sum of the ages of three of them is 115, what's the age of the fourth man?

pashok25 [27]

Answer:

35

Step-by-step explanation:

if 1 man is 37

and 1 man is 43

the 3rd man is 45

they add to 115

to average 40, we gotta add 35

this old mans giving u that!

3 0

2 years ago

On a winter day in Alaska, the temperature at noon was -0.6°C. From noon to 3:00, the temperature increased by 1.2°C. From 3:00

vazorg [7]

The expression is -6 + 1.2 + -0.4 + -0.6

7 0

3 years ago

10. Find the area of the shaded region.

Semenov [28]

Answer:

Area = 114

Step-by-step explanation:

We first must find the area of the larger outside rectangle.

Area = length × width

15 × 8 = 120

Then we find the area of the smaller inside rectangle.

4 × 1.5 = 6

Since the small rectangle is not shaded we have to subtract its area from the larger shaded rectangle's area.

120 - 6 = 114

8 0

3 years ago

What bigger meter or yad

Ivenika [448]

Meter is 39.37 inches

Yard is 36 inches

3 0

3 years ago

Read 2 more answers

What is the biweekly salary equivalent to a monthly salary of ​$3434.08

What is the biweekly salary equivalent to a monthly salary of $3434.08