Answer:
a) min = 4.4251
b) max = 8.5743
Step-by-step explanation:
Given:
Mean, u = 6.5
Standard deviation = 1
To get our values, we are to use the inverse of the standard normal table.
a) The minimum head breadth that will fit.
P(Z < z) = 1.9%
P(Z < z) = 0.019
P(Z < -2.0749) = 0.019
z = -2.0749
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = -2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (-2.0749 * 1) + 6.5
x = 4.4251
The minimum head breadth that will fit the clientele is 4.4251
b) The maximum head breadth that will fit.
P(Z > z) = 1.9%
1 - P(Z < z) = 0.019
P(Z < z) = 1 - 0.019 = 0.981
P(Z < 2.0749) = 0.981
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = 2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (2.0749 * 1) + 6.5
x = 4.4251
x = 8.5743
The maximum head breadth that will fit the clientele is 8.5743
