Question

A) If a normal distribution has a mean µ = 40 and a standard deviation σ = 2, what value of x would you expect to find 2 standard deviations below the mean

B) If a normal distribution has a mean µ = 70 and a variance σ2 = 16, what value of x would you expect to find 2.5 standard deviations above the mean?

C)If a sample yields a mean xmean = 44 and we know that the sum of all x values = 2772, what must the sample size be?

D)If a sample of 36 observations yields a variance s2 = 4, what must the sum of the squared deviations from the mean be equal to?

Answer 1

A.

= 40

= 2

we know that an std. normal variable Z is:

Z = (X-)/

At 2 standard deviations below the mean:

z = -2

(x-)/ = -2

x = - 2*

= 40-4

= 36

B.

= 70

² = 16

= 4

we know that an std. normal variable Z is:

Z = (X-)/

At 2.5 standard deviations above the mean:

z = 2.5

(x-)/ = 2.5

x = +  2.5*

= 70+10

= 80

C.

= 44

= 2772

Let the no. of observations be n, then

= /n

n = /

= 2772/44

= 63

D.

n = 36

s² = 4

We know that,

Sum of squared deviation from mean, SSD =

s² = SSD/(n-1)

So,

SSD = (n-1)*s²

= 35*4

= 140

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