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Sagot :
The probability that x will be less than 55 is 0.1587.
Given,
In the Question;
X is a normally distributed random variable .
Mean µ = 50
Standard deviation (σ) = 5
X = 55
To solve the probability that x will be less than 55.
Now, According to the question:
The standardize the Random Variable X with the Standardized Normal Distribution Z Variable using the relationship:
Z = (X - µ) ÷ σ
Normal Distribution Tables of the function:
Φ(z) = P(Z ≤ z)
P(X > 55) = P(Z > ((55 - 50) ÷ 5))
P(X > 55) = P(Z > 5 ÷ 5)
P(X > 55) = P(Z > 1)
So,
P(X > 55) = P(Z > 1)
P(X > 55) = 1 - P(Z < 1)
Using the Standard Normal Table,
P(X > 55) = 1 - Φ(1)
P(X > 55) = 1 - 0.8413
P(X > 55) = 0.1587
Hence, The probability that x will be less than 55 is 0.1587.
Learn more about the Normal distribution at:
https://brainly.com/question/13759327
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