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3. A grocery store manager is told by the wholesaler that the apples in a large...

3. A grocery store manager is told by the wholesaler that the apples in a large shipment have a mean weight of 6 ounces and a standard deviation of 1 ounce. The manager randomly selects 100 apples.

a. assuming the wholesaler’s claim is true, find the probability that the mean weight of the sample is more than 5.9 ounces

b. the manager plans to return the shipment if the mean weight is less than 5.75 ounces. Assuming the wholesaler’s claim is true, find the probability that the shipment will be returned.

Math   Statistics-And-Probability   
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Answer #1

Let X be the weight of apples in a large shipment

X~ Normal ( 6, 1 )

A random sample 100 apples is selected

Let be the mean weight of the sample

~ Normal ( 6, = 0.1 )

a) P( > 5.9) = P( > )

= P( z > -1)

= P( z < 1)

= 0.84134

b) Probability ( the shipment will be returned.) = P( < 5.75)

=P( < )

= P( z < -2.5)

= 1- P( z < 2.5)

= 1- 0.99379

= 0.00621

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