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

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 6.9 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 6.2 and 7.3 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. 19% of the time, a customer will buy a bag of California oranges that weighs more than a specific weight. Find that weight.

math   Statistics-And-Probability   
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Answer Date: 22/01/2019 a) The probability that a randomly selected California orange bag purchased by a customer weighs more than 8 pounds is, First, compute the z score then find probability based on standardnormal table. For x - 8 converts to 8-6.9 V1.21 1.00 From the standard normal distribution table, the associated probability is 0.8413. Since find the area to the right, so subtract from 1 to getP(z >1.00) -1- (z <1.00) 1-0.8413 = 0.1587 The probability that a randomly selected California orange bag purchased by a customer weighs more than 8 pounds is 0.1587 b) The probability that a randomly selected California orange bag purchased by a customer weighs between 6.2 and 7.3 pounds is, First, compute the z score then find probability based on standard normal table. Forx 6.2 converts to 6.2 6.9 1.21 0.64For x 7.3 converts to 7.3-6.9 1.21 0.36 From the standard normal distribution table, the associated probability for z values and subtracts the probabilityis, p(6.2 s x s 7.3) p(-0.64 šzs0.36) - p(z < 0.36)- p(z-0.64) 0.6406-0.2611 0.3795 The probability that a randomly selected California orange bag purchased by a customer weighs between 6.2 and 7.3 pounds is 0.3795. c)The probability that a randomly selected California orange bag purchased by a customer weighs exactly 5 pounds is, First, compute the z score then find probability based on standard normal table. For x - 5 converts to 5-6.9 V1.21 From the standard normal distribution table, the associated probability for the area to the left is shown below, p(z1.73) 0.0418 The probability that a randomly selected California orange bag purchased by a customer weighs exactly 5 pounds is 0.0418 d)The weight is, From the standard nomal table, the indicated z score for the area of 0.1900 subtract from 1 and indicative area 0.8100 is 0.88. -6.9(0.88x 1.21) - 7.87 The weight is 7.87

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