6x 2 y<br> 6d - 2d +3e<br> 5 x h

The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning at

tamaranim1 [39]

Answer:

Between 0.01 and 0.20

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

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:

$n = 500, p = 0.05$

So

$\mu = E(X) = np = 500*0.05 = 25$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]
Find the probability of winning at least 30 times.Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)$ . So this is 1 subtracted by the pvalue of Z when X = 29.5. Then

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

$Z = \frac{29.5 - 25}{4.8734}$

$Z = 0.92$

$Z = 0.92$ has a pvalue of 0.8212

1 - 0.8212 = 0.1788

So the correct option is:

Between 0.01 and 0.20

7 0

3 years ago

What is 15 of 250% percent of what number

german

Assuming the question is: '15 is 250% of what number'.

We can write an equation.

'is' indicates an equal sign

'of' indicates multiplication

'what number' indicates an unknown number we can call 'x'

So we have:

15 = 250% * x

or

15 = 2.5x

Divide 2.5 to both sides:

x = 6

4 0

3 years ago

Martha biked 55 miles per day and Enrico biked 145 miles every 3 days. After 6 days, which statement correctly compares the numb

masha68 [24]

Answer:

After 6 days Martha biked 330 miles, while Enrico biked 290 miles.

Step-by-step explanation:

i. Martha bikes 55 miles per day.

So that after 6 days, Martha would have covered;

55 miles x 6 = 330 miles

After 6 days, Martha would have biked 330 miles.

ii. Enrico bikes 145 miles every 3 days.

Then after 6 days, Enrico would have covered;

$\frac{6 days}{3 days}$ x 145 miles

= 2 x 145 miles

= 290 miles

After 6 days, Enrico would have biked 290 miles.

After 6 days Martha biked 330 miles, while Enrico biked 290 miles.

7 0

3 years ago

HELP PLEASE will givr=e brainiest

Kruka [31]

Answer:

You spend $180 on pants and shirts. You pay $12 per pair of pants (x) and $15 per shirt (y). You buy 6 more pairs of pants

4 0

3 years ago

What is the value of x in the equation 5x−6=−36?

Montano1993 [528]

Answer:

5x−6=−36

5x=-30

X=-6

5*(-6)-6=-36

-30-6=-36

-36=-36

Your Welcome

BIFFY OUT!!!

7 0

3 years ago

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6x 2 y 6d - 2d +3e 5 x h