When crossing the Golden Gate Bridge, traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f(x)
0.11.-0.11%
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a. What is the mean waiting time that drivers face when entering San Francisco via the Golden Gate Bridge? (Round your answer to 2
decimal places.)
Mean waiting time
b. What is the probability that a driver spends more than the average time to pay the toll? (Round intermediate calculations to at least
4 decimal places and final answer to 4 decimal places.)
Probability
c. What is the probability that a driver spends more than 18 minutes to pay the toll? (Round intermediate calculations to at least 4
decimal places and final answer to 4 decimal places.)
Probability

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: