Question

A tire company test a particular model of tire and finds the tires to be normally distributed it with respect to wear. The mean is 28,000 miles and the standard deviation is 2500 miles. If 2000 tires are tested about how many are likely to wear out before 23,000 miles

Answer 1

Deejilani, this is the solution to the problem:

The information provided to us:

Mean = 28,000

S.D = 2,500

Number of tires = 2,000

Distance of cut-off (x) = 23,000

Step 1: Let's calculate the z-score, as follows:

z = (x - Mean)/Standard Deviation

z = (23,000 - 28,000)/2,500

z = -5,000/2,500

z = -2

Step 2: Now we calculate the Probability of z = -2, using the z-table, this way:

P (x < 23,000) = 0.02275

Step 3: Now we find the number of tires that are likely to wear out before 23,00 miles, as follows:

2,000 * 0.02275 = 45.5

Rounding to the next integer because tires cannnot be a decimal number: 46 tires are likely to wear out before 23,000 miles