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Thepotemich [5.8K]

3 years ago

11

Erma has 5/12 of a carton of eggs in the refrigerator. She uses 3/12 of the carton to make an omelet. What fraction of the carto

n of eggs is left

2 answers:

Rus_ich [418]3 years ago

7 0

Answer:2/12

Step-by-step explanation: subtrack the numb'

Sergio [31]3 years ago

6 0

You subtract the numerators so the answer is 2/12

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According to a recent Census Bureau report, 12.7% of Americans live below the poverty level. Suppose you plan to sample at rando

larisa [96]

Answer:

a) $P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b) $P(X \leq 10) = 0.2614$

c) $(1-0.127)^7 (0.127) =0.0491$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=100, p=0.127)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

a. What is the probability that you count exactly 10 in poverty?

For this case we want this probability P(X=10)

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b. What is the probability that you count 10 or less in poverty? .2614

For this case we want this probability $P(X=\leq10)$

$P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)$

And we can find the individual probabilities like this:

$P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}$

$P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}$

$P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132$

$P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629$

$P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222$

$P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620$

$P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143$

$P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279$

$P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471$

$P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701$

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

And then repplacing we got:

$P(X \leq 10) = 0.2614$

c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected? .0491

For this case we need after 7 people , 1 in poverty so we can find this probability like this:

$(1-0.127)^7 (0.127) =0.0491$

7 0

3 years ago

A contractor purchases 3 dozen pairs of padded work gloves for $42.48. He incorrectly calculates the unit price as $14.16 per

Harrizon [31]

Answer:

1.18

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the surface area of the cone to the nearest whole number? Use 3.14 for π.

IRISSAK [1]

Hello!

We know that surface area of a cone = pi(r^2) + pi(rL) where L is the Slant height and R is the Radius and h is Height.
So, 30 is height, and half of 32 is the radius, then we just plug and chug,

An in Short, Your Answer would be 2512, Option "A"

Hope this Helps! :)

5 0

4 years ago

Read 2 more answers

In 1985, American swimmer Tom jager completed a 50- meter freestyle swim in 22.40 seconds. In 1990, he was able to complete the

puteri [66]

Tom was slow by 1.2 seconds

6 0

3 years ago

a photograph is printed in the center of a piece of paper measuring 7 cm by (x + 8) cm. The photo measures 5 cm by (x +6) cm . T

Nadusha1986 [10]

The paper is 7 cm by (x + 8) cm.

A photo is 5 cm by (x + 6) cm, and is printed in the middle of the paper.

The area of the border/space around the photo is 50 cm².

To find the area of the border around the photo, you find the area of the paper and subtract it by the area of the photo.

The area of the paper:

A = 7 · (x + 8)

The area of the photo:

A = 5 · (x + 6)

Your equation to find the area of the border around the photo is:

(7 · (x + 8)) - (5 · (x + 6)) = A

[area of paper - area of photo = area of border]

Since you know the area of the border, you can plug it in:

(7 · (x + 8)) - (5 · (x + 6)) = 50

Multiply the 7 into (x + 8), and multiply the 5 into (x + 6)

(7x + 56) - (5x + 30) = 50

Distribute/multiply the - to (5x + 30)

7x + 56 - 5x - 30 = 50

Combine like terms

2x + 26 = 50

Subtract 26 on both sides

2x = 24

Divide 2 on both sides

x = 12

7 0

3 years ago