Question

A random sample is drawn from a normally distributed population with mean μ = 20 and standard deviation σ = 2.5. Use Table 1.

a.	Is the sampling distribution of the sample mean with n = 28 and n = 55 normally distributed?
	Yes No

b.	Can you use the standard normal distribution to calculate the probability that the sample mean is less than 20.6 for both sample sizes?
	Yes No

c.	Calculate the above probabilities for both sample sizes. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

n	Probability
28
55

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 2.5

a ) Yes,

b )Yes,

c )n = 28

= 20

  =  ( /n) = (2.5 / 28 ) = 0.4725

P (   < 20.6 )

P ( - /) < (20 - 20.6 /  0.4725)

P ( z < - 0.6/ 0.4725 )

P ( z < -1.27 )

Using z table

= 0.1020

Probability = 0.1020

n = 55

= 20

  =  ( /n) = (2.5 / 55 ) = 0.3371

P (   < 20.6 )

P ( - /) < (20 - 20.6 / 0.3371)

P ( z < - 0.6/ 0.3371 )

P ( z < -1.78 )

Using z table

= 0.0375

Probability = 0.0375