The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1000 miles. what warranty should the company use if they want 96% of the tires to outlast the warranty? 59,000 miles 58,250 miles 61,000 miles 61,750 miles

61,750 miles

Step-by-step explanation:

Given : The p-value of the tires to outlast the warranty = 0.96

The probability that corresponds to 0.96 from a Normal distribution table is 1.75.

Mean :

Standard deviation :

The formula for z-score is given by  : -

Hence, the tread life of tire should be 61,750 miles if they want 96% of the tires to outlast the warranty.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm