Question

Suppose a certain population of observations is normally distributed. What percentage of the observa- tions in the population(a) are within;1.5standard deviations of the mean?(b) are more than 2.5 standard deviations above themean?(c) are more than 3.5 standard deviations away from (above or below) the mean?

Answer 1

Answer:

Step-by-step explanation:

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

WE can use standard normal distribution table to get the required probabilities and hence percent.

a)P(within 1.5 std dev from the mean) = P(|z|<1.5) =2(0.4332)

=0.8664 =86.64%

b) P(more than 2.5 std dev above the mean) = P(Z>2.5) = 0.5-0.4938

=0.0062=0.62%

c) P(More than 3.5 std dev away from above or below the mean)

=P(|z|>3.5) <2(0.5-0.4990) = 0.0020

i.e. <0.2%

Answer 2

If the population is normally distributed, the percentage of observations that are within 1.5 standard deviations are 0.8664.

The percentage more than 2.5 standard deviations are 0.0062.

The percentage more than 3.5 standard deviations are 0.0005.

What percentage of the population are within 1.5 standard deviations?

= P (Z ± 1.5)

= 0.9332 - (1-0.9332)

= 0.8664.

What percentage of the population are more than 2.5 standard deviations?

= P (Z > 2.5)

= 1 - 0.9938

= 0.0062.

What percentage of the population are more than 3.5 standard deviations?

= P (Z > 3.5) + P (Z < - 3.5)

= 0.0005.

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