Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.

(a) are within + 1.5 standard deviations of the mean?

(b) are more that 2.5 standard deviations above the mean?

(c) are more that 3.5 standard deviations away from (above or below) the mean?

Question

Mathematics

Amir Romero

11 January, 17:34

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.

(a) are within + 1.5 standard deviations of the mean?

(b) are more that 2.5 standard deviations above the mean?

(c) are more that 3.5 standard deviations away from (above or below) the mean?

+3

Answers (1)

Know the Answer?

Bryant Spencer · Answer 1

For the standard normal distribution Z, the mean μ = 0

and σ the standard deviation = 1

a) P (0 ≤ Z ≤ 1.5) →P (Z=1.5) - P (Z=0)

P (0 ≤ Z ≤ 1.5) = 0.9332 - 0.5 = 0.4322

b) P (Z ≥ 2.5) →P (Z=2.5) = 1 - P (Z=2.5)

P (Z ≥ 2.5) = 1 - 0.9938 = 0.0062

c) P (Z≥ 3.5) = 1 - P (Z = 3.5) = 0

OR P (Z≤ 3.5) = 0