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4 years ago

C−12>−4 ...................................

Mathematics

2 answers:

WITCHER [35]4 years ago

6 0

Add 12 to each side

so it should be C>8

alexandr402 [8]4 years ago

4 0

C can be anything over 8. C minus 12 has to be greater than -4 so then replace C with a random number, say 10. We do 10-12 which is -2 which is greater than 4

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

frosja888 [35]

Answer:

a) 0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

b) 0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

c) 0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday

d) 0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

Step-by-step explanation:

We solve this question using the normal approximation to the binomial distribution.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed distributions 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

Sample of 723, 3.7% will live past their 90th birthday.

This means that $n = 723, p = 0.037$ .

So for the approximation, we will have:

$\mu = E(X) = np = 723*0.037 = 26.751$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{723*0.037*0.963} = 5.08$

(a) 15 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 15 - 0.5) = P(X \geq 14.5)$ , which is 1 subtracted by the pvalue of Z when X = 14.5. So

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

$Z = \frac{14.5 - 26.751}{5.08}$

$Z = -2.41$

$Z = -2.41$ has a pvalue of 0.0080

1 - 0.0080 = 0.9920

0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 30 - 0.5) = P(X \geq 29.5)$ , which is 1 subtracted by the pvalue of Z when X = 29.5. So

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

$Z = \frac{29.5 - 26.751}{5.08}$

$Z = 0.54$

$Z = 0.54$ has a pvalue of 0.7054

1 - 0.7054 = 0.2946

0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

This is, using continuity correction, $P(25 - 0.5 \leq X \leq 35 + 0.5) = P(X 24.5 \leq X \leq 35.5)$ , which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 24.5. So

X = 35.5

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

$Z = \frac{35.5 - 26.751}{5.08}$

$Z = 1.72$

$Z = 1.72$ has a pvalue of 0.9573

X = 24.5

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

$Z = \frac{24.5 - 26.751}{5.08}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.3300

0.9573 - 0.3300 = 0.6273

0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday.

(d) more than 40 will live beyond their 90th birthday

This is, using continuity correction, P(X > 40+0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

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

$Z = \frac{40.5 - 26.751}{5.08}$

$Z = 2.71$

$Z = 2.71$ has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

6 0

3 years ago

Francis gets 6 paychecks in 12 weeks. How many paychecks does she get in 52 weeks?

Darya [45]

First, figure out how long it takes Francis to get one paycheck.
You do this by dividing the number of weeks by the number of paychecks.
12 ÷ 6 = 2
Now, you divide 52 weeks by the time it takes to get one paycheck.
52 ÷ 2 = 26
This means that Francis gets 26 paychecks in 52 weeks.

3 0

3 years ago

Carl is on the school track team. To prepare for an upcoming race, he plans to run 207 miles total over the next 31 days. Write

Mkey [24]

207 divide 31 = 6.7 miles per day
y= days
x= distance
y=6.7

8 0

3 years ago

Enter numbers to complete rows 0 through 6 of Pascal triangle

Svet_ta [14]

Answer:

1. Use Pascal's Triangle to expand the binomial.

(d – 3)6

d6 – 18d5 + 135d4 – 540d3 + 1,215d2 – 1,458d + 729

d6 + 18d5 + 135d4 + 540d3 + 1,215d2 + 1,458d + 729

d6 – 6d5 + 15d4 – 20d3 + 15d2 – 6d + 1

d6 + 6d5 + 15d4 + 20d3 + 15d2 + 6d + 1

2. Use the Binomial Theorem to expand the binomial. (3v + s)5

s5 – 5s4v + 10s3v2 – 10s2v3 + 5sv4 – v5

s5 + 15s4v + 90s3v2 + 270s2v3 + 405sv4 + 243v5

s5 + 45s4v + 270s3v2 + 810s2v3 + 1,215sv4 + 729v5

s5 + 15s4 + 90s3 + 270s2 + 405s + 243

3. What is the fourth term of (d – 4b)3?

–b3

64b3

–64b3

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

I need help!! im struggling with this question

postnew [5]

Answer:

1 gallon : 25.6 miles

Step-by-step explanation:

So, the way we can find the rate, or ratio between 2 units is to divide one unit by the other unit.

So basically, we see the first set of units is:

2 gallons - 51.2 miles

So basically, for every 2 gallons, there are 51.2 miles.

To find the ratio, or rate, we must find the miles per gallon.

We can do that by dividing both sides by 2:(g=gallons, m=miles)

2g/2=51.2/2m

g=25.6

So for every gallon, there is 25.6 miles.

We can write this as:

1 : 25.6

Hope this helps!

3 0

3 years ago

Read 2 more answers