Please show all your work. Thank you! 2. notices that the time it takes for her

Question

Please show all your work. Thank you!

2. notices that the time it takes for her to get to school is normally distributed with a mean of 40 minutes and a standard deviation minutes. She is interested to know the of 5 following: a. What is the probability that she will take exactly 48 minutes to get to school? b. Assume on Monday she leaves home at 7:25. What is the probability that she will arrive at school before 8? c. Assume she left home at 7: 25. What is the probability that she will arrive at school after 8:15? d. LeAnn s school begins each morning at 8:30. What time should she leave home to be 99% confident that she will arrive on time?

Explanation / Answer

here for normal distribution Z=(X-mean)/std deviation

a) P(X=48)=0 ; as it is a continuous distribution and provide interval probabilty as area under the interval. cause a point does not have any area under it, the probability correspond to it is 0

b)P(X<35)=P(Z<(35-40)/5)=P(Z<-1)=0.1587

c)P(X>50)=1-P(X<50) =1-P(Z<(50-40)/5)=1-P(Z<2)=1-0.9772=0.0228

d)for 99% confidence , at 99% ; z=2.3263

hence time taken corresponding to this =mean +z*std deviation =51.63~52 minutes

therefore she should start at (8:30-52)=7:38

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