Question

Suppose that a random sample of size 64 is to be selected from a population with mean 50 and standard deviation 7. (Use a table or technology.)

(a)

What are the mean and standard deviation of the

x

sampling distribution?

μ_x

σ_x

=

(b)

What is the approximate probability that

x

will be within 0.5 of the population mean μ? (Round your answer to four decimal places.)

(c)

What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)

Answer 1

a)

Mean =50

Standard deviation = 7/ sqrt(64)  

= 7/8 =0.875

b)

µ =    50                              
σ =    0.875                              
we need to calculate probability for ,                                  
P (   49.5   < X <   50.5   )                  
=P( (49.5-50)/0.875 < (X-µ)/σ < (50.5-50)/0.875 )                                  
                                  
P (    -0.571   < Z <    0.571   )                   
= P ( Z <    0.571   ) - P ( Z <   -0.571   ) =    0.7161   -    0.2839   =    0.4323

c)

µ =    50              
σ =    0.875              
                  
P ( X ≥   50.80   ) = P( (X-µ)/σ ≥ (50.8-50) / 0.875)          
= P(Z ≥   0.914   ) = P( Z <   -0.914   ) =    0.1803
= 0.1803 *2

= 0.3606