1) The area under a normal curve is equal to 1 (100%). True or False 2) The diam
ID: 3372001 • Letter: 1
Question
1) The area under a normal curve is equal to 1 (100%).
True or False
2) The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter less than 2.15 inches?
a. 0.9554 b. 0.0446 c. -3.85 d. -1.7
3) The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter greater than 3.76 inches?
a. 0.9357 b. 0.0125 c. 1.52 d. 0.0643
a. 0.9357 b. 0.0125 c. 1.52 d. 0.0643
Explanation / Answer
1) The area under a normal curve = 1 . TRUE
2) z = (x - mean) / std deviation . Here x = 2.15, mean = 3, std dev = 0.5
z = (2.15 - 3)/0.5 = -1.7 . From the z table , p (x<2.15) =0.0446 (b)
3) z = (x - mean) / std deviation . Here x = 3.76, mean = 3, std dev = 0.5
z = (3.76 - 3)/0.5 = 1.52 . From the z table , p (x<3.76) =0.9357 , therefore p(x>3.76) = 1 - p(x<3.76)
p(x>3.76) = 1 - 0.9357 = 0.0643 (d)
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