In: Statistics and Probability
A particular fruit's weights are normally distributed, with a mean of 422 grams and a standard deviation of 35 grams. If you pick one fruit at random, what is the probability that it will weigh between 386 grams and 541 grams
Solution :
Given that ,
mean =
= 422
standard deviation =
= 35
n = 1
= 422
=
/
n= 35 /
1=35
P(386< <541
) = P[(386-422) /35 < (
-
) /
< (541-422) /35 )]
= P( -1.03< Z <3.4 )
= P(Z <3.4 ) - P(Z <-1.03 )
Using z table
=0.9997-0.1515
=0.8482
probability=0.8482