Question

The charges for utility bills for all households in a town have a skewed probability distribution with a mean of $158 and a standard deviation of $27. Find the probability that the mean amount due on utility bills for a random sample of 71 households selected from this town city will be

a. between $150 and $154
  

b. within $5 of the population mean.
  

c. more than the population mean by at least $4
  

Round your z values to 2 decimal places before looking them up in the table or using them in a calculator.

Keep 4 decimal places in your final answers.

Answer 1

mena = 158 , s = 27 , n = 71

a)

P(150 < x< 154)
= P((150 -158) /(27/sqrt(71)) < z < (154 -158) /(27/sqrt(71))

= P(-2.50 < z < -1.25)
= P(z< -1.25) - P(z< -2.50)
= 0.0997

b)

P(158 - 5 < x < 158+5)
= P(153 < x < 163)
= P((153 -158) /(27/sqrt(71)) < z < (163 -158) /(27/sqrt(71))

= P(-1.56< z < 1.56)
= P(z< 1.56) - P(z< 1.56)
= 0.8813

c)

P(x> 4)
= P(z > (162 - 158)/(27/sqrt(71))
= P(z> 1.25)
= 0.1060