Question

Given that x is a normal variable with mean μ = 52 and standard deviation σ = 6.5, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c) P(50 ≤ x ≤ 60)

Find z such that 15% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 10.0 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 7 and 11 minutes


(b) the response time is less than 7 minutes


(c) the response time is more than 11 minutes

Answer 1

1)a)

probability =P(X<60)=(Z<(60-52)/6.5)=P(Z<1.23)=0.8907

b)

probability =P(X>50)=P(Z>(50-52)/6.5)=P(Z>-0.31)=1-P(Z<-0.31)=1-0.3783=0.6217

c)

probability =P(50<X<60)=P((50-52)/6.5)<Z<(60-52)/6.5)=P(-0.31<Z<1.23)=0.8907-0.3783=0.5124

2)

a)

probability =P(7<X<11)=P((7-10)/1.5)<Z<(11-10)/1.5)=P(-2<Z<0.67)=0.7486-0.0228=0.7258

b)

probability =P(X<7)=(Z<(7-10)/1.5)=P(Z<-2)=0.0228

c)

probability =P(X>11)=P(Z>(11-10)/1.5)=P(Z>0.67)=1-P(Z<0.67)=1-0.7486=0.2514