Need work shown please Use the following to answer the next

Use the following to answer the next two exercises: The cost of unleaded gasoline in the Ray Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Ray Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas cations. 83. What\'s the approximate probability that the average price for 16 gas stations is over $4.691 a. almost zero b. 0.1587 C. 0.0943 d. unknown

Solution

Mean ( u ) =4.59
Standard Deviation ( sd )=0.1
Number ( n ) = 16
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 4.69) = (4.69-4.59)/0.1/ Sqrt ( 16 )
= 0.1/0.025= 4
= P ( Z >4) From Standard Normal Table
= 0                  

almost zero