Solution :
Given that,
standard deviation = =6.87
Margin of error = E = 1.5
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
sample size = n = [Z/2* / E] 2
n = ( 1.96* 6.87 / 1.5)2
n =80.58=81
b.
Sample size = n =138
Margin of error = E = 2
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645
sample size = n = [Z/2* / E] 2
n = ( 1.645 * 6.87 / 2 )2
n =31.92899
Sample size = n =32
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