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Shkiper50 [21]
4 years ago
10

Heinrich is a vacuum cleaner salesman. For each vacuum cleaner he sells, he receives $7. If he sells between 30 and 40 vacuum cl

eaners a month, about how much will he earn in a month?
Mathematics
1 answer:
Semmy [17]4 years ago
5 0

Hi! This is just a simple multiplication problem!

So he recieves 7 dollars for each vacuum cleaner therefore we must multiply 7 by the amount he sells.

7*30 =210

7*35=245

7*40 280

That means he will earn somewhere between 210 dollars - 280 dollars

Hope this helped!

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Answer:

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Answer:

a) P(X=14)=(20C14)(0.8)^{14} (1-0.8)^{20-14}=0.109

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The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

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The probability mass function for the Binomial distribution is given as:

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Part a

For this case we want this probability:

P(X=14)

And using the mass function we have this:

P(X=14)=(20C14)(0.8)^{14} (1-0.8)^{20-14}=0.109

Part b

For this case we want this probability:

P(X \geq 10)

And we can find this using the complement rule:

P(X\geq 10) = 1-P(X

P(X=0)=(20C0)(0.8)^{0} (1-0.8)^{20-0}=1.05x10^{-14}

P(X=1)=(20C1)(0.8)^{1} (1-0.8)^{20-1}=8.39x10^{-13}

P(X=2)=(20C2)(0.8)^{2} (1-0.8)^{20-2}=3.19x10^{-11}

P(X=3)=(20C3)(0.8)^{3} (1-0.8)^{20-3}=7.65x10^{-10}

P(X=4)=(20C4)(0.8)^{4} (1-0.8)^{20-4}=1.30x10^{-8}

P(X=5)=(20C5)(0.8)^{5} (1-0.8)^{20-5}=1.66x10^{-7}

P(X=6)=(20C6)(0.8)^{6} (1-0.8)^{20-6}=1.66x10^{-6}

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P(X \leq 16)= 1-P(X>16) =1-P(X \geq 17)= 1- [P(X=17) +...+P(X=20)]

P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205

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And if we replace we got:

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Part d

The expected value is given by:

E(X)= np = 20 *0.8 = 16

Var(X) = np(1-p) = 20*0.8*(1-0.8) = 3.2

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