period of time, it has been determined that the police response time has a emerg

Question

period of time, it has been determined that the police response time has a emergency call, find the following (a) the response time is between 5 and 10 minutes (Round your answers to four decimal places.) a mean of 8 2 minutes and·standard deviation of 2 o-nes, rar a received (b) the response tieve is less than S minutes (c) the response time is more than 10 minutes months and a st After many years (a) If Quick Start your a full refund on any battery that failswithin the 36-month period after purchase, what percentage of its batteries wi the company expect to replace Run answer to two decimal places.) (b) If Quick Start does not want to make nearest month)? refunds for more guarantee the batteries (to the

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 8.2
standard Deviation ( sd )= 2
a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5) = (5-8.2)/2
= -3.2/2 = -1.6
= P ( Z <-1.6) From Standard Normal Table
= 0.0548
P(X < 10) = (10-8.2)/2
= 1.8/2 = 0.9
= P ( Z <0.9) From Standard Normal Table
= 0.8159
P(5 < X < 10) = 0.8159-0.0548 = 0.7611
b.
P(X < 5) = (5-8.2)/2
= -3.2/2= -1.6
= P ( Z <-1.6) From Standard Normal Table
= 0.0548
c.
P(X > 10) = (10-8.2)/2
= 1.8/2 = 0.9
= P ( Z >0.9) From Standard Normal Table
= 0.1841

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