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2 years ago

Aj jar of sweets contains 5 yellow sweets, 4 red sweets, 8 green sweets 4 orange sweets and 3 white sweets.

Mathematics

2 answers:

LuckyWell [14K]2 years ago

7 0

Answer:

$\frac{9}{24}$

Step-by-step explanation:

Add all the sweets together ( that will be your denominator )

5+4+8+4+3= 24

The probability she will pick and yellow and orange ( add those numbers together)

Yellow + orange = Numerator

5+4=9

How you answer should be lay out :

$\frac{Orange+ yellow sweets}{Total amount of sweets}$

Alisiya [41]2 years ago

4 0

Answer:

9/24

Step-by-step explanation:

add the sweets (for denominator) 5+4+8+4+3 =24 then add yellow + orange (which is 9)

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According to a 2014 Gallup poll, 56% of uninsured Americans who plan to get health insurance say they will do so through a gover

Airida [17]

Answer:

a) 24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange

b) 0.1% probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange

c) Expected value is 560, variance is 246.4

d) 99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

Step-by-step explanation:

To solve this question, we need to understand the binomial probability distribution and the binomial approximation to the normal.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

56% of uninsured Americans who plan to get health insurance say they will do so through a government health insurance exchange.

This means that $p = 0.56$

a. What is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange?

This is P(X = 6) when n = 10. So

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

$P(X = 6) = C_{10,6}.(0.56)^{6}.(0.44)^{4} = 0.2427$

24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange

b. What is the probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange?

This is P(X = 600) when n = 1000. So

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

$P(X = 600) = C_{1000,600}.(0.56)^{600}.(0.44)^{400} = 0.001$

0.1% probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange

c. What are the expected value and the variance of X?

$E(X) = np = 1000*0.56 = 560$

$V(X) = np(1-p) = 1000*0.56*0.44 = 246.4$

d. What is the probability that less than 600 people plan to get health insurance through a government health insurance exchange?

Using the approximation to the normal

$\mu = 560, \sigma = \sqrt{246.4} = 15.70$

This is the pvalue of Z when X = 600-1 = 599. Subtract by 1 because it is less, and not less or equal.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{599 - 560}{15.70}$

$Z = 2.48$

$Z = 2.48$ has a pvalue of 0.9934

99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

4 0

2 years ago

I need assistance solving these questions using Cramers' Rule (which I am frankly terrible at) and need these to finish my homew

Scrat [10]

Answer:

What are the questions?

3 0

3 years ago

Read 2 more answers

The diagram below shows the rectangle PLUM.

Illusion [34]

Answer:

Area of rectangle PLUM = 75.00 square units

Step-by-step explanation:

Since diagonal of rectangle divides the rectangle into two equal triangles,

Therefore, area of the rectangle PLUM = 2× area of triangle PLM

By the mean proportional theorem,

In ΔPLM,

AP² = AM × AL

6² = AM × 8

AM = $\frac{36}{8}$

AM = 4.5 units

Area of PLM = $\frac{1}{2}(\text{Base})(\text{height})$

= $\frac{1}{2}(ML)(AP)$

= $\frac{1}{2}(8 + 4.5)(6)$

= 12.5 × 3

= 37.5 units²

Now area of rectangle PLUM = 2×37.5 = 75 units²

Therefore, area of the rectangle is 75.00 square units.

3 0

2 years ago

What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?

Bess [88]

Answer:

(4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

4 0

2 years ago

22. Every hour, Jennifer can sew 24 dresses

JulsSmile [24]

Answer:

2.5 hours

Step-by-step explanation:

24 + 20 = 44

110 divided by 44 = 2.5

3 0

2 years ago