79%-) 4:29 PM .11 T-Mobile Done 4 of 11 (4)A certain brand of a car is tested fo

Question

79%-) 4:29 PM .11 T-Mobile Done 4 of 11 (4)A certain brand of a car is tested for breaking distances. From past statistical data, it is known the 60-to-0 distance' (the shortest distance to have a complete stop from 60miles/hour) obeys a normal distribution with a mean of 100 feet and the ‘variance, of 51 . Suppose in a random test drive a car (of the same brand) applies full brakes at a speed of 60 miles per hour a) [4 points] What is the probability that the car stops within a range of 91 feet? b) [4 points] What is the probability that the car needs more than 110 feet to get to a complete stop? c) [4 points] If the driver applies the break to avoid a collision with an object appeared 105 feet ahead, what is the probability that he/she would avoid the collision successfully? (Assume that "lane departure is not allowed during the drive.) e

Explanation / Answer

here std deviaiton =(51)1/2 =7.1414

a) probability =P(X<91)=P(Z<(91-100)/7.1414)=P(Z<-1.2603)=0.1038

b)P(X>110)=1-P(X<110)=1-P(Z<(110-100)/7.1414)=1-P(Z<1.4003)=1-0.9193=0.0807

c)

P(X<105)=P(Z<(105-100)/7.1414)=P(Z<0.7001)=0.7581

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