Question

Some data have a distribution that is symmetric and bell-shaped, a mean value of 5.5. We know that 95% of the data is between 4.3 and 6.7. Use the 95% rule to find the standard deviation.

Answer 1

The standard deviation σ = 0.6122

Explanation:

Explanation:-

Given mean of the Population = 5.5

we know that 95% of confidence interval of Z-score = 1.96

95% of confidence interval for mean in normal distribution

(μ±Z₀.₉₅σ)

(μ - 1.96σ , μ +1.96σ)

given that 95% of confidence interval between 4.3 and 6.7

μ - 1.96σ = 4.3

5.5 -1.96σ = 4.3

5.5 - 4.3 = 1.96σ

1.2 = 1.96σ

σ =
`(1.2)/(1.96)`

The standard deviation σ = 0.6122