Question

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The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?
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Answer 1

Probability that the total weight exceeds the maximum weight = 1/2

Step-by-step explanation:

Mean = 60 kg

SD = 10 kg

Weight on truck = 650 kg

Number of goats = 10

Total weight of goat on truck = 10 * 60 = 600

SD is 10

Assuming + 10 for all 10 goats, total weight = 700

The truck can accommodate up to 650 kg.

So if more than 5 goats are overweight, then the truck will be overloaded.

Probability that the total weight exceeds the maximum weight = 5/10 = 1/2