Question

1. Given N(14, 3), answer the following questions.
(pictured below)

Answer 1

1) 98% 2)68% 3)50% 4)83.9%

Explanation:

we would apply the formula for normal distribution which is expressed as z = (x - µ)/σWherex = variableµ = mean outputσ = standard deviationFrom the information given, µ = 14σ = 31) P(x < 20)For x = 20, z = (20 - 14)/3 = 2From the normal distribution table, the corresponding probability value is 0.98% = 0.98 × 100 = 98%

2) P(11 ≤ x ≤ 17)For x = 11, z = (11 - 14)/3 = - 1From the normal distribution table, the corresponding probability value is 0.16For x = 17, z = (17 - 14)/3 = 1From the normal distribution table, the corresponding probability value is 0.84P(11 ≤ x ≤ 17) = 0.84 - 0.16 = 0.68% = 0.68 × 100 = 68%

3) P(x > 14) = 1 - P(x ≤ 14)For x = 14, z = (14 - 14)/3 = 0From the normal distribution table, the corresponding probability value is 0.5P(x > 14) = 1 - 0.5 = 0.5% = 0.5 × 100 = 50%

4) P(5 ≤ x ≤ 17)For x = 5, z = (5 - 14)/3 = - 3From the normal distribution table, the corresponding probability value is 0.00135For x = 17, z = (17 - 14)/3 = 1From the normal distribution table, the corresponding probability value is 0.84P(5 ≤ x ≤ 17) = 0.84 - 0.00135 = 0.839% = 0.839 × 100 = 83.9%

Answer 2

1) 98%

2)68%

3)50%

4)83.9%