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3 years ago

13

A round swimming pool (a cylinder) has a diameter of 16 feet and a height of 4 feet. How many gallos of water can the pool hold

if 1ft cubed = 7.5 gallons?

1 answer:

Marina CMI [18]3 years ago

8 0

If my calculations aren't off, it is approximately 80.43.

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Step-by-step explanation:

Since the trials are independent, this is a binomial distribution:

<u>Recall:</u>

Binomial Distribution --> $P(k)={n\choose k}p^kq^{n-k}$
$P(k)$ denotes the probability of $k$ successes in $n$ independent trials
$p^k$ denotes the probability of success on each of $k$ trials
$q^{n-k}$ denotes the probability of failure on the remaining $n-k$ trials
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<u>Given:</u>

$n=10$
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$p^k=0.53^4$
$q^{n-k}=(1-0.53)^{10-4}=0.47^6$
${n\choose k}={10\choose 4}=\frac{10!}{(10-4)!4!}=210$

<u>Calculate:</u>

$P(4)=(210)(0.53^4)(0.47^6)=0.1786117069\approx0.179$

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