The diameter of oranges in a certain orchard are normallydistributed with a mean
ID: 2918976 • Letter: T
Question
The diameter of oranges in a certain orchard are normallydistributed with a mean of 5.00 inches and a standard deviation of0.50 inches. Show all work. a) What percentage of the oranges in this orchard havediameters less than 6.8 inches? b) What percentage of the oranges in this orchard are largerthan 4.90 inches? c) A random sample of 100 oranges is gathered and the meandiameter obtained was 4.90? If another sample of 100 is taken, whatis the probability that its sample mean will be greater than 5.10inches? d) Why is the z-score used in answering (a), (b), and(c)? e) Why is the formula for z used in (c) different from thatused in (a) and (b)? The diameter of oranges in a certain orchard are normallydistributed with a mean of 5.00 inches and a standard deviation of0.50 inches. Show all work. a) What percentage of the oranges in this orchard havediameters less than 6.8 inches? b) What percentage of the oranges in this orchard are largerthan 4.90 inches? c) A random sample of 100 oranges is gathered and the meandiameter obtained was 4.90? If another sample of 100 is taken, whatis the probability that its sample mean will be greater than 5.10inches? d) Why is the z-score used in answering (a), (b), and(c)? e) Why is the formula for z used in (c) different from thatused in (a) and (b)?Explanation / Answer
a) What percentage of the oranges in this orchard havediameters less than 6.8 inches?P(X<6.8) = P((X-)/ <(6.8-5)/0.5) = P(Z<3.6) = 0.9998 (99.98%) (check normaltable)
b) What percentage of the oranges in this orchard are largerthan 4.90 inches?
P(X>4.9) = P(Z>(4.9-5)/0.5) = P(Z>-0.2)= 0.5793 (57.93%) (check normal table)
c) A random sample of 100 oranges is gathered and the meandiameter obtained was 4.90? If another sample of 100 is taken, whatis the probability that its sample mean will be greater than 5.10inches?
P(xbar > 5.10)=P((xbar-)/(/n) >(5.1-5)/(0.5/sqrt(100))) = P(Z>2) =0.0228 (check normaltable)
d) Why is the z-score used in answering (a), (b), and (c)?
The diameter of oranges in a certain orchard arenormally distributed.
e) Why is the formula for z used in (c) different from thatused in (a) and (b)?
In (c), it is calculated for the probability ofthe sample mean.