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 7.7 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 8 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?

c. 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. 20% of the time, a customer will buy a bag of California oranges that weighs more than a specific weight. Find that weight.

Explanation / Answer

mean = 7.7 , variance = 1.21, std. deviation = 1.1

a)

P(X>8)

z = ( x - mean) / s

= (8 - 7.7) / 1.1

= 0.27

P(X> 8) = P(z > 0.27) = 0.3925

b)

P(6.1 < X < 7.2)

z = ( x - mean) / s

= (6.1 - 7.7) / 1.1

= -1.45

z = ( x - mean) / s

= (7.2 - 7.7) / 1.1

= -0.45

P(6.1 < X < 7.2 ) = P(-1.45 < Z < -0.45) = 0.2518

c)

P(4.95 < X < 5.05)

z = ( x - mean) / s

= (4.95 - 7.7) / 1.1

= -2.5

z = ( x - mean) / s

= (5.5 - 7.7) / 1.1

= -2

P(4.95< X<5.5) = P(-2.5 < Z <-2) = 0.0165

d)

z value at 20% = 0.84

x bar = mean + z*s

= 7.7 + 0.84 * 1.1

= 8.624

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