contestada

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?

Respuesta :

mreijepatmat
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

Cricetus

The required percentages are:

(a) 86.64%

(b) 0.62%

(c) 0.04%

With the use of standard normal table, we can find the required percentage, such as:

(a)

→ [tex]P( -1.5<z<1.5)= P( z <1.5)- p( z < -1.5)[/tex]

                                 [tex]= 0.9332-0.0668[/tex]

                                 [tex]= 0.8664[/tex]

                                 [tex]= 86.64[/tex] (%)

(b)

→ [tex]P( z >2.5)=0.0062[/tex]

                    [tex]= 0.62[/tex] (%)

(c)

→ [tex]P( z < -3.5) + p( z > 3.5) = 0.0002+0.0002[/tex]

                                           [tex]= 0.0004[/tex]

                                           [tex]=0.04[/tex] (%)  

Thus the above approach is right.

Learn more about standard deviation here:

https://brainly.com/question/16555520

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