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3 years ago

What is the best estimate for the product of 279 and 7

Mathematics

1 answer:

shutvik [7]3 years ago

4 0

Answer:

279 × 7 ≈ 2800

Step-by-step explanation:

if you have to round to the tens place, then both would be rounded up, the 7 to 10 and the 279 to 280. 10 × 280 = 2800

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Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

spayn [35]

Answer:

60.26% probability that less than twenty students are absent

Step-by-step explanation:

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 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 120, p = 0.15$ .

$\mu = E(X) = np = 120*0.15 = 18$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.15*0.85} = 3.91$

If a random sample of 120 names is called on a Monday, what is the probability that less than twenty students are absent?

This is the pvalue of Z when X = 20-1 = 19. So

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

$Z = \frac{19 - 18}{3.91}$

$Z = 0.26$

$Z = 0.26$ has a pvalue of 0.6026.

60.26% probability that less than twenty students are absent

3 0

3 years ago

A rock is thrown from the top of a tall building.The distance in feet between the rock and the ground t seconds after thrown is

marusya05 [52]

Answer:

0.448 seconds

Step-by-step explanation:

d = -16t² -4t + 412

find t when d = 407

substituting d = 407 into the equation:

407 = -16t² -4t + 412 (subtract 407 from both sides)

-16t² -4t + 412 - 407 = 0

-16t² -4t + 5 = 0 (multiply both sides by -1)

16t² + 4t - 5 = 0

solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with

t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)

t = (-1/8) (1 -√21) = 0.448 seconds (answer)

4 0

3 years ago

What is the value of q in the equation? A) -10/7 B) 10/7 C)6 D) 10

cricket20 [7]

q=10

Remove the radical by raising each side to the index of the radical

Hope this helps!

6 0

3 years ago

Read 2 more answers

According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Dmitry_Shevchenko [17]

Using z-scores, it is found that the value of z is z = 1.96.

-----------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean $\mu$ and standard deviation $\sigma$ , is given by:

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

It measures how many standard deviations the measure is from the mean.
Each z-score has an associated p-value, which is the percentile.

The normal distribution is symmetric, which means that the middle 95% is between the 2.5th percentile and the 97.5th percentile.
The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

7 0

2 years ago

A electrician charges $45 per hour and spends $20 a day on gasoline.Write an algebraic expression to represent his earnings for

Sliva [168]

(45 X 24) - 20

hope this helps!

3 0

3 years ago

Read 2 more answers