Question

Find the interval [ μ−z σn√,μ+z σn√μ−z⁢ σn,μ+z⁢ σn ] within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

(a) μ = 179, σ = 10, n = 33. (Round your answers to 2 decimal places.)
  
The 95% range is from   to  .

(b) μ = 867, σ = 18, n = 10. (Round your answers to 2 decimal places.)
  
The 95% range is from   to  .

(c) μ = 63, σ = 4, n = 27. (Round your answers to 3 decimal places.)
  
The 95% range is from   to  .

Answer 1

Solution :

Given that,

a) mean = = 179

standard deviation = = 10

n = 33

= = 179

= / n = 10 / 33 = 1.74

P( - 2 < <   + 2 ) = 95%

= P( 179 - 2 * 1.74 < < 179 + 2 * 1.74 ) = 95%

= P( 179 - 3.48 < < 179 + 3.48 ) = 95%

=P( 175.52 < < 182.48 ) = 95%

b) mean = = 867

standard deviation = = 18

n = 10

= = 867

= / n = 18 / 10 = 5.69

P( - 2 < <   + 2 ) = 95%

= P( 867 - 2 * 5.69 < < 867 + 2 * 5.69 ) = 95%

= P( 867 - 11.38 < < 867 + 11.38 ) = 95%

=P( 855.62 < < 878.38 ) = 95%

c) mean = = 63

standard deviation = = 4

n = 27

= = 63

= / n = 4 / 27 = 0.770

P( - 2 < <   + 2 ) = 95%

= P( 63 - 2 * 0.770 < < 63 + 2 * 0.770 ) = 95%

= P( 63 - 1.540 < < 63 + 1.540 ) = 95%

=P( 61.460 < < 64.540 ) = 95%