1\"Suppose tha what number? aZ follows a standard normal distribution. The proba

Question

1"Suppose tha what number? aZ follows a standard normal distribution. The probability is 10% that Z is greater than 2.A company can purchase raw material from either Supplier A or Supplier B and is concerned about the amounts of impurity the material contains. A review of the records for each supplier indicates that the percentage impurity levels in consignments of the raw material follow normal distributions with the means and standard deviations given in the table below. The company is particularly anxious that the impurity level in a consignment not exceed 5% and want to purchase from the supplier more likely to meet that specification. Which supplier should be chosen? Supplier A: Mean: 4.4 Standard D: 0.4 Supplier B: Mean 4.2 Standard D: 0.6 3.The tread life of a particular brand of tires has a normal distribution with mean 40,000 miles and standard deviation 5,000 miles. What proportion of these tires will have tread lives between 35,000 and 45,000 miles? What proportion of these tires will have tread lives between 30,000 and 50,000 miles?

Explanation / Answer

1) Solution :

Given that Z follows the standard normal distributuion .

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

To see the probabilityb 0.90. in the standard normal table the corresponding z value is 1.28 .

P(Z < 1.28) = 0.90

That number is 1.28

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