In: Statistics and Probability
A particular fruit's weights are normally distributed, with a
mean of 515 grams and a standard deviation of 28 grams.
If you pick 4 fruit at random, what is the probability that their
mean weight will be between 470 grams and 557 grams (Give answer to
4 decimal places.)
Solution :
Given that ,
mean =
= 515
standard deviation =
= 28
n = 4
= 515
=
/
n= 28 /
4=14
P(470< <
557) = P[(470-515) / 14< (
-
) /
< (557-515) / 14)]
= P(-3.21 < Z <3 )
= P(Z <3 ) - P(Z <- 3.21)
Using z table
=0.9987-0.0007
=0.9980
probability=0.9980