Mathematics, 06.04.2020 16:56, kordejah348

A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of $10.50 and a standard deviation of $5.20. He usually waits on about 50 parties over a weekend of work. a) Estimate the probability that he will earn at least $600. b) How much does he earn on the best 1% of such weekends?

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answered: Scienceissofun6453

(a) The probability that he will earn at least $600 is 0.0212.

(b) The amount of tip the waiter earns on the best 1% of such weekends is $610.67.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{X}=n\mu$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{X}=\sqrt{n}\sigma$

The random variable X can be defined as the tips he receiver per order.

The average tip received by the waiter is, μ = $10.50.

The standard deviation of the tip received by the waiter is, σ = $5.20.

The waiter usually waits on about n = 50 parties over a weekend of work.

So, the distribution of the total tip earned by the waiter is:

$\sum X\sim N(\$525,\ \$36.77)$ .

(a)

Compute the probability that he will earn at least $600 as follows:

$P(\sum X\geq 600)=P(\sum X600-0.5)$

$=P(\sum X599.5)\\$

$=P(\frac{\sum X-\mu_{X}}{\sigma_{X}}\frac{599.5-525}{36.77})$

$=P(Z2.03)\\=1-(Z$

*Use a z-table for the probability.

Thus, the probability that he will earn at least $600 is 0.0212.

(b)

Let be a be the amount of tip the waiter earns on the best 1% of such weekends.

That is,

P (∑X > a) = 0.01

⇒ P (∑X < a) = 0.99

⇒ P (Z < z) = 0.99

The value of z for the above probability is:

z = 2.33.

Compute the value of a as follows:

$z=\frac{a-\mu_{X}}{\sigma_{X}}$

$2.33=\frac{a-525}{36.77}$

$a=525+(2.33\times 36.77}\\a=610.6741\\a\approx610.67$

Thus, the amount of tip the waiter earns on the best 1% of such weekends is $610.67.

answered: Guest

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that $\frac{ab}{de}=\frac{bc}{ef}$ .

also, it is given that $\frac{ab}{de}=\frac{3}{4}$

so, from the options, we need that $\frac{bc}{ef}=\frac{3}{4}$ .

a. $\frac{bc}{ef}=\frac{6}{9}=\frac{2}{3}$

b. $\frac{bc}{ef}=\frac{4}{6}=\frac{2}{3}$

c. $\frac{bc}{ef}=\frac{8}{12}=\frac{2}{3}$

d. $\frac{bc}{ef}=\frac{12}{16}=\frac{3}{4}$

as, we can see that only option d gives the same ratio as $\frac{ab}{de}=\frac{3}{4}$ i.e. $\frac{bc}{ef}=\frac{3}{4}$ .

hence, the possible lengths are bc = 12 and ef = 16.

answered: Guest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.