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use z score to find percentage or probability

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The weight of 3rd grade children is normally distributed with a mean of 64 and a standard deviation of 10. Two children are selected at random from a very large population.

(a.) What is the probability that both will weigh more than 70 pounds?
(b.) What is the probability that one of the children will weigh more than 65 pounds and the other will weigh less than 59 pounds?
(c.) Assume that a school bus can hold 36 children and has a maximum weight capacity (excluding the driver) of 2340 pounds. Assume that 36 randomly selected children board the bus. What is the probability that the total weight of these children will exceed the weight capacity of the bus?

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Solution Preview

Hi there,

Here is my answer:

(a)
z=(x-mean)/standard deviation=(70-64)/10=0.6
the probability of one kid weighing more than 70 pounds
P(z>0.6)=1-0.7257=0.2743.

since ...

Solution Summary

The solution uses a z score to find out the percentage or probability.

$2.19