A small publisher wishes to publish self-improvement books. After a survey of the market, the publisher finds that the average cost of the type of book that she wishes to publish is $15.00. If she wants to price her books to sell in the middle 64% range, what should the maximum and minimum prices of the books be? The standard deviation is $0.25 and the variable is normally distributed.

Maximum price of book will be $15.23

Minimum price of book will be $14.77.

Step-by-step explanation:

We are given that a small publisher wishes to publish self-improvement books. After a survey of the market, the publisher finds that the average cost of the type of book that she wishes to publish is $15.00. The standard deviation is $0.25 and the variable is normally distributed.

Also, she wants to price her books to sell in the middle 64% range.

The above situation represents that we want 64% confidence interval for the price of book which she wants to publish.

Firstly, the pivotal quantity for 64% confidence interval for the population mean is given by;

                          P.Q. =  ~ N(0,1)

where, = sample average cost of the type of book = $15

            = population standard deviation = $0.25

            n = sample of book = 1

             = population mean

Here level of significance =   = 18%

Here for constructing 64% confidence interval we have used One-sample z test statistics because we know about population standard deviation.

So, 64% confidence interval for the population mean, is ;

P(-0.9195 < N(0,1) < 0.9195) = 0.64  {As the critical value of z at 18%

                                           level of significance are -0.9195 & 0.9195}  

P(-0.9195 < < 0.9195) = 0.64

P( < < ) = 0.64

P( < < ) = 0.64

64% confidence interval for = [ , ]

                                       = [ , ]

                                       = [$14.77 , $15.23]

Therefore, the maximum price of book will be $15.23 and the minimum price of book will be $14.77.