Answer:
(a) The sampling distribution of is given by;
~ Normal ( )
(b) P( > 87.8) = 0.0287
Step-by-step explanation:
We are given that a simple random sample of size equals 49 is obtained from a population with mu equals 84 and sigma equals 14.
<em><u>Let </u></em><em><u> = sample mean</u></em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = 84
= standard deviation = 14
n = sample size = 49
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
(a) The sampling distribution of is given by;
~ Normal ( )
(b) Probability of greater than 87.8 is given by = P( > 87.8)
P( > 87.8) = P( > ) = P(Z > 1.90) = 1 - P(Z 1.90)
= 1 - 0.9713 = <u>0.0287</u>
The above probability is calculated by looking at the value of x = 1.90 in the z table which has an area of 0.9713.