Answer:
(1) 0.4207
(2) 0.7799
Step-by-step explanation:
Given,
Mean value,
[tex]\mu = 15.0[/tex]
Standard deviation,
[tex]\sigma = 1.25[/tex]
(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)
[tex]= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})[/tex]
[tex]=1-P(z\leq \frac{17.5 - 15}{1.25})[/tex]
[tex]=1-P(z\leq \frac{2.5}{1.25})[/tex]
[tex]=1-P(z\leq 2)[/tex]
[tex]=1- 0.5793[/tex] ( By using z-score table )
= 0.4207
(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)
[tex]=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})[/tex]
[tex]=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})[/tex]
[tex]=P(z\leq 2.4) - P(z\leq -0.8)[/tex]
= 0.9918 - 0.2119
= 0.7799
The probabiliity that the force is greater than 17.5 kips is 2.28% while the probabiliity that the force is between 14 and 18 kips is 20.37%
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Mean value 15.0 (kips) and standard deviation 1.25 (kips).
1) For 17.5:
z = (17.5 - 15) / 1.25 = 2
P(x > 17.4) = 1 - P(z < 2) = 1 - 0.9772 = 0.0228
2) For 14:
z = (14 - 15)/1.25 = 0.8
For 18:
z = (18 - 15)/1.25 = 2.4
P(14 < x < 18) = P(z < 2.4) - P(z < 0.8) = 0.9918 - 0.7881 = 0.2037
The probabiliity that the force is greater than 17.5 kips is 2.28% while the probabiliity that the force is between 14 and 18 kips is 20.37%
Find out more on z score at: https://brainly.com/question/25638875
