Question

3. The average weight of 80 randomly selected potatoe chip packages is 98.5gm. Historically the package weights have a standard deviation of 5.3gm. The manufacturer believes that the average package weight is 100gm. Assuming the CLT applies and = 100, calculate the probability of obtaining a sample mean less than 98.5gm

Answer 1

solution:

given

$\mu$ = 100

$\sigma$ = 5.3

n = 80

To find P(
T
< 98.5):

=p(
T
-$\mu$/$\sigma$ /
n
<98.5-100/ 5.3/
00
)

=p(z<-1.5/0.592558)

=p(z<-2.5313)

=1-p(z<2.5313)

=1-0.9943(from table)

=0.0057