Question

Find the probability and interpret the results. If​ convenient, use technology to find the probability. During a certain week the mean price of gasoline was ​$2.717 per gallon. A random sample of 32 gas stations is drawn from this population. What is the probability that the mean price for the sample was between ​$2.69 and ​$2.72 that​ week? Assume σ equals=​$0.047. The probability that the sample mean was between $2.696 and ​$2.728 is

Answer 1

given mean=2.717

Standard Deviation=0.047

n=32

Here we take the distribution as normal distribution. Hence,

p(z1<z<z2)=p((2.69-2.717)/(0.047/sqrt(32))<(x-2.717)/(0.047/sqrt(32))<(2.72-2.717)/(0.047/sqrt(32))

=p(-3.25<z<0.36

=p(z=0.36)-p(z=-3.25)

=0.5254-0.2828

=0.2426.

p(z1<z<z2)=p((2.696-2.717)/(0.047/sqrt(32))<(x-2.717)/(0.047/sqrt(32))<(2.728-2.717)/(0.047/sqrt(32))

=p(-2.53<z<1.32)

=p(z=1.32)-p(z=-2.53)

=0.5925-0.3275

=0.265

=0.2426.