Question

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.9 ounces and a standard deviation of 1.1 ounces.

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.5 ounces. Round your answer to 4 decimal places.


(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 8.9 ounces. Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean =   = 7.9

standard deviation = = 1.1

n = 5

= 7.9

=  / n = 1.1/ 5=0.4919

P( <9.5 ) = P[( - ) / < (9.5-7.9) / 0.4919]

= P(z <3.25 )

Using z table  

= 0.9994   

probability= 0.9994

(B)

n = 6

= 7.9

= / n = 1.1/ 6 = 0.4491

P( >8.9 ) = 1 - P( <8.9)

= 1 - P[( - ) / < (8.9 -7.9) / 0.4491]

= 1 - P(z <2.23)

Using z table

= 1 - 0.9871

= 0.0129

probability= 0.0129