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MaRussiya [10]
3 years ago
8

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean valu

e 15.0 (kips) and standard deviation 1.25 (kips). Calculate the following probabilities: (1) (2 points) P(X ≥ 17.5). (2) (2 points) P(14 ≤ X ≤ 18).
Mathematics
1 answer:
Sauron [17]3 years ago
8 0

Answer:

(1) 0.4207

(2) 0.7799

Step-by-step explanation:

Given,

Mean value,

\mu = 15.0

Standard deviation,

\sigma = 1.25

(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)

= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})

=1-P(z\leq \frac{17.5 - 15}{1.25})

=1-P(z\leq \frac{2.5}{1.25})

=1-P(z\leq 2)

=1- 0.5793   ( By using z-score table )

= 0.4207

(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)

=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})

=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})

=P(z\leq 2.4) - P(z\leq -0.8)

= 0.9918 - 0.2119

= 0.7799

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