Question

In a certain normal distribution, find the standard deviation σ when μ = 50 and 10.56% of the area lies to the right of 55.

Answer 1

Answer:

4

Step-by-step explanation:

P(x > 55) = 0.1056

P(x < 55) = 1 − 0.1056

P(x < 55) = 0.8944

z = 1.25

z = (x − μ) / σ

1.25 = (55 − 50) / σ

σ = 4

Answer 2

The value of the standard deviation in the distribution given is 4

• The mean, μ = 50
• The standard deviation, σ =?
• P(x > 55) = 0.1056 ( Area to the right)

The equivalent expression using the area to the left is :

• P(x < 55) = 1 - P(x > 55)
• P(x < 55) = 1 - 0.1056
• P(x < 55) = 0.8944

Using normal distribution table:

• Zscore for P(Z < 0.8944) = 1.25

Recall :

• Zscore = (x - μ) ÷ σ
• x = 55 ;
• 1.25 = (55 - 50) / σ
• 1.25σ = 5
• Divide both sides by 1.25
• σ = 4

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