Question

Given N(14, 3)

% below 20 =

% between 11 and 17 =

% above 14 =

% between 5 and 17 =


PLZ HELP

Answer 1

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

Explanation:

Answer 2

Explanation:

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = variable

µ = mean output

σ = standard deviation

From the information given,

µ = 14

σ = 3

1) P(x < 20)

For x = 20,

z = (20 - 14)/3 = 2

From 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 = - 1

From the normal distribution table, the corresponding probability value is 0.16

For x = 17,

z = (17 - 14)/3 = 1

From the normal distribution table, the corresponding probability value is 0.84

P(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 = 0

From the normal distribution table, the corresponding probability value is 0.5

P(x > 14) = 1 - 0.5 = 0.5

% = 0.5 × 100 = 50%

4) P(5 ≤ x ≤ 17)

For x = 5,

z = (5 - 14)/3 = - 3

From the normal distribution table, the corresponding probability value is 0.00135

For x = 17,

z = (17 - 14)/3 = 1

From the normal distribution table, the corresponding probability value is 0.84

P(5 ≤ x ≤ 17) = 0.84 - 0.00135 = 0.839

% = 0.839 × 100 = 83.9%