Question

Suppose xx has a distribution with a mean of 205 and a standard deviation of 32. Random samples of size n=64n=64 are drawn.

a) Describe the ¯xx¯ distribution.

• ¯xx¯ will have a normal distribution since the sample size n≥30n≥30.
• ¯xx¯ will have a uniform distribution since the xx-distribution is normal.
• ¯xx¯ will have a uniform distribution since the sample size n≥30n≥30.
• ¯xx¯ will have a normal distribution since the xx-distribution is normal.

b) Compute the mean of the ¯xx¯-distribution.
μ¯x=μx¯=

c) Compute the standard deviation of the ¯xx¯-distribution.
σ¯x=σx¯=

d) Compute P(¯x>213)P(x¯>213).  (Round to 4 decimal places.)

e) Would it be unusual for a random sample of size 64 from the x−x- distribution to have a sample mean greater than 213?

• It's not unusual since P(¯x>213)P(x¯>213) ≤0.05≤0.05
• It's not unusual since P(¯x>213)P(x¯>213) >0.05>0.05
• It's unusual since P(¯x>213)P(x¯>213) >0.05>0.05
• It's unusual since P(¯x>213)P(x¯>213) ≤0.05

Answer 1

Solution :

Given that,

mean = = 205

standard deviation = = 32

n = 64

a) will have a normal distribution since the sample size n ≥ 30

b) = = 205

c) = / n = 32 / 64 = 4

P( > 213 ) = 1 - P( < 213)

= 1 - P[( - ) / < (213 - 205) /4 ]

= 1 - P(z < 2.00)

Using z table,    

= 1 - 0.9772

= 0.0228

e) It's unusual since P( >213) ≤ 0.05