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# Normal Probability distribution

Problem 1)

The weigh of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces.

a) What is the probability that a shoe weighs more than 13 ounces?
b) What must the standard deviation of weght be in order for the company to state that 99.9% of its shoes are leass than 13 ounces?
c) If the standard deviation remains at 0.5 ounces, what must the mean weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?

Problem 2)

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inches and a standard deviation of 0.0004 inches.

a) What is the probability that the diameter of a dot exceeds 0.0026?
b) What is the probability that a diameter is between 0.0014 and 0.0026 inches?
c) What standard deviation od diameters is needed so that the probability in part (b) is 0.995?

#### Solution Preview

Please refer attached file for complete solution. Work done with the help of equation writer may not print here.

Problem 1) the weigh of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounces.

a) What is the probability that a shoe weighs more than 13 ounces?
Let X denotes the weight of shoe.
Mean = =12 ounces
Standard deviation = =0.5 ounces
Tables for normal distribution are standardized.
Z=
We have to find P(X>13)

Now standardize X with the help of above formula,
Z= (13-12/0.5) =2

P(X>13) =P(Z>2)

Look in standardized normal distribution tables for z=2
We get value of 0.4772
We know that this is probability for z being in between 0 and 2.
and P(Z>0) =0.5

P(Z>2) =0.5-0.4772=0.0228

b) What must the standard deviation of weight ...

#### Solution Summary

Solution describes the steps for finding probabilities of given events with the help of normal distribution.

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