Question

Consider a normal distribution curve where the middle 65 % of the area under the curve lies above the interval ( 3 , 17 ). Use this information to find the mean, μ , and the standard deviation, σ , of the distribution. a) μ= b) σ=

Answer 1

Mean = μ = 10

Standard deviation = σ = 18.42

Explanation:

We know that in normal distribution,

μ ± z*σ

Where μ is the mean, σ is the standard deviation and z is the corresponding z-score

Upper value = μ + z*σ

Lower value = μ - z*σ

The z-score corresponding to 65 percentile is 0.38

17 = μ + 0.38*σ eq. 1

3 = μ - 0.38*σ eq. 2

Add eq. 1 and eq. 2

20 = 2μ

μ = 20/2

μ = 10

substitute μ = 10 into eq. 1

17 = 10 + 0.38*σ

0.38*σ = 17 - 10

σ = 7/0.38

σ = 18.42

Therefore, the mean is 10 and standard deviation is 18.42