# Statistics -6 | Mathematics homework help

Homework #6

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Use the following scenario to answer the next 3 questions.  Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch.   A sample of 25 bags is selected. So we have that the breaking strength of the bags is normal with µ=5 lbs/in2 and σ = 1.5 lbs/in2.   Also, n = 25.

1)         What is the probability that the average breaking strength is between 5 and 5.5 pounds per square inch?

2)         What is the probability that the average breaking strength is between 4.2 and 4.5 pounds per square inch?

3)         What is the probability that the average breaking strength is less than 4.6 pounds per square inch?

Use the following scenario to answer the next 3 questions.  Historically, 93% of the deliveries of an overnight mail service arrive before 10:30 the following morning.   Random samples of 500 deliveries are selected.  So we have a “historic” (read: population) proportion of p = .93.

Also, n = 500.

4)         What proportion of the samples will have between 93% and 95% of the deliveries arriving before 10:30 the following morning?

5)         What proportion of the samples will have more than 95% of the deliveries arriving before 10:30 the following morning?

6)         What is the proportion of the samples will have less than 90% of the deliveries arriving before 10:30 the following morning?

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