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

Mila Arias

6 May, 22:21

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?

Judith Pineda · 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