Question

If the sample mean is 9 hours, the population st deviation is 3.5 hours and the sample size is 50, then the 95% confidence interval is approximately

a. 7.04 to 110.96 hours

b. 7.36 to 10.64 hours

c. 7.80 to 10.20 hours

none of the above

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is

a. Zero

b. (a / b)

c. (b / a)

d. 1/(b/a)

Z is a standard normal random variable. The P(0.90 < z < 1.20) equals

a. 0.4678

b. 0.0436

c. 0.8527

d. None of the Above

Answer 1

Solution :

Given that,

1) Point estimate = sample mean = = 9

Population standard deviation =    = 3.5

Sample size = n = 50

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 3.5/  50 )

= 0.97

At 90% confidence interval estimate of the population mean is,

  ± E

9 ± 0.97   

( 8.03, 9.97 )  

d) none of the above

2) Using Uniform distribution,

f(x) = 1 / b - a

correct option is = d

3) Using standard normal table,  

P( 0.90 < Z < 1.20)

= P( Z < 1.20) - P( Z < 0.90)

= 0.8849 - 0.8159

= 0.0690

d. None of the Above