A grocery store purchases bags of oranges from California to sell in their store

Question

A grocery store purchases bags of oranges from California to sell in their store. The weight of a bag of California oranges is normally distributed with a mean of 8.6 pounds and a variance of 1.21 pounds2. A bag of California oranges is randomly selected in the grocery store Round all probability answers to four decimal places.) a. What is the probability that a randomly selected California orange bag purchased by a customer weighs more than 7 pounds? b. What is the probability that a randomly selected California orange bag purchased by a customer weighs between 6.1 and 7.2 pounds? . What is the probability that a randomly selected California orange bag purchased by a customer weighs exactly 5 pounds? Round weight to two decimal places) d. 21% of the time, a customer will buy a bag of California oranges that weighs more than a specific weight. Find that weight.

Explanation / Answer

a)

P(x>7)=P(Z>(7-8.6)/1.1)=P(Z>-1.45)=0.9265 ( please try 0.9271 if thos comes wrong)

b)

P(6.1<X<7.2)=P(-2.27<Z<-1.27)=0.0904 (please try 0.0900 if this comes wrong)

c)

P(X=5)=0 (as point probability is 0 for continuous funciton)

d)

for top 21% ; critical z =0.81

hence corresponding weight =8.6+0.81*1.1 =9.49

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