The average salary for a certain profession is $75,500. Assume that the standard deviation of such salaries is $30,500. Consider a random sample of 71 people in this profession and let x over bar x represent the mean salary for the sample.
a. |
What is mu Subscript x over barμ x ? |
mu Subscript x overbarμxequals=?
b. |
What is sigma Subscript x over bar σ x? |
sigma Subscript x over bar σ x=________(Round to two decimal places as needed.)
c. |
Describe the shape of the sampling distribution of x over bar x. |
A. The shape is that of a uniform distribution.
B. The shape is that of a poisson distribution.
C. The shape is that of a normal distribution.
D.The shape is that of a binomial distribution.
d. |
Find the z-score for the value x over bar x =68,000. |
z=____________(Round to two decimal places as needed.)
e. |
Find Px>68,000 = ________(Round to three decimal places as needed. |
Answer
(a) is the population mean, which is given in the question. So, we can write it as = 75,500
(b) is the population standard deviation, which is given in the question. So, we can write it as = 30,500
(c) Option C is correct because data is normally distributed with mean value 75500 and standard deviation = 30500
(d) Formula for z score is given as
where = 75,500, = 30,500, n = 71 and = 68000
setting the given values, we get
(rounded to two decimals)
(e) Now, we have to find the value of
Using the identity
we can write it as
(using z distribution table)
(we find 2.00 in the left most column and 0.07 in the top most row in z distribution, then selected the intersection value)
So, p value is 0.981 (rounded to 3 decimals)
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