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earnstyle [38]
3 years ago
8

The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.711.7 fluid

ounces and a standard deviation of 0.20.2 fluid ounce. A drink is randomly selected. Find the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces.
Mathematics
1 answer:
dexar [7]3 years ago
5 0

Answer:  0.1499

Step-by-step explanation:

Given : The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with mean \mu=11.7\text{ fluid ounces}

Standard deviation : \sigma=0.2\text{ days}

z-score : z=\dfrac{X-\mu}{\sigma}

For X = 11.5  

z=\dfrac{11.5-11.7}{0.2}\approx-1

For X = 11.6  

z=\dfrac{11.6-11.7}{0.2}\approx-0.5

Now, the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces will be :-

P(11.5

Hence, the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces =0.1499

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11. The sum S of the first n consecutive positive integers, 1, 2, 3, ... , n, is given by the formula S=0.5n(n+1). Find n when S=120 and check your answer by addition.

120 = \frac 1 2 n (n+1)

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n^2 + n -240 = 0

We need two numbers whose sum is 1 and multiply to -240, so two numbers whose difference is 1 and multiply to 240, 15 and 16. We factor:

(n+16)(n-15)= 0

n=-16 \textrm{ or } n=15

We reject the negative root.

n=15

Check:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15

=1+15 + 2+14 + 3+13 + 4+12 + 5+11 +6+10 + 7+9 + 8

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13. A boat travels downstream (with the current) for 36 miles and then makes the return trip upstream (against the current). The trip downstream took 3/4 of an hour less than the upstream trip. If the rate of the current is 4 mph, find the rate of the boat in still water and the time for each part of the trip.

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Writing our equation,

3/4 = 36/(v-4) - 36/(v+4)

3 = 144 (1/(v-4) - 1/(v+4))

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Time upstream is 36/(20-4)=36/16=9/4 = 2.25 hours

3/4 hour difference, good

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