Question

The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.3 ounce.

​(a) What is the probability that a randomly selected carton has a weight greater than 8.09 ​ounces?

​(b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 8.09

ounces?

Answer 1

Solution :

P(x >8.09 ) = 1 - P(x<8.09 )

= 1 - P[(x -) / < (8.09-8) /0.3 ]

= 1 - P(z < 0.3)

Using z table

= 1 -  0.6179

probability= 0.3821

(b)

n=16

= =8

= / n = 0.3/ 16 = 0.075

P( >8.09 ) = 1 - P( <8.09)

= 1 - P[( - ) / < (8.09-8) /0.075 ]

= 1 - P(z < 1.2)

Using z table

= 1 - 0.8849

= 0.1151

probability= 0.1151