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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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