3ciii I am unsure of In a certain town the number of children, X, in a family ch

Question

3ciii I am unsure of

In a certain town the number of children, X, in a family chosen at random has the following

distribution:

a) Find the mean and variance of X.

b) State the approximate distribution for the number of children in 100 families.

c) If a group of 100 families is chosen at random what are the approximate probabilities there will be

i. more than 150 children

ii. present between 160 and 180 children present.

ii. iii.When catering for the children the organisers wish to be 95% certain that they have provided enough food for the children. How many children should they cater for?

Explanation / Answer

mean = summation of (x * p)
= 0*0.2 + 1 * 0.3 + 2 * 0.3 + 3 * 0.1 + 4 * 0.1
= 1.6

Variance = summation of ( x^2p - mean^2)
= (0^2 * 0.2 + 1^1 * 0.3 + 2^2 * 0.3 + 3^2 * 0.1 + 4^2 * 0.1) - 1.6^2
= 1.44
std.deviation = sqrt ( variance) = 1.2

3) z value at 95% CI = 1.96

x = mean + z * s
= 1.6 + 1.96 * 1.2
= -0.752
  

3. c. iii)

For 100 families, expected (mean) number of children = 1.6*100 = 160

std. dev. = s*sqrt(n) = 1.2*sqrt(100) = 12

z value at 95% (right tail) = 1.64

x = mean + z*s = 160 + 1.64*12 = 179.68

Hence 180 students will be catered for 95%.

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