Find the probability and interpret the results. If? convenient, use technology t
ID: 3367918 • Letter: F
Question
Find the probability and interpret the results. If? convenient, use technology to find the probability.
The population mean annual salary for environmental compliance specialists is about
?$64 comma 000
.
A random sample of
35
specialists is drawn from this population. What is the probability that the mean salary of the sample is less than
?$61 comma 500
??
Assume
sigma
equals?$6 comma 000
.
The probability that the mean salary of the sample is less than
?$61 comma 500
is
nothing
.
?(Round to four decimal places as? needed.)
Interpret the results. Choose the correct answer below.
A.
Only
0.69
?%
of samples of
35
specialists will have a mean salary less than
?$61 comma 500
.
This is an
unusual
event.
B.
About
0.69
?%
of samples of
35
specialists will have a mean salary less than
?$61 comma 500
.
This is not an unusual event.
C.
About
69
?%
of samples of
35
specialists will have a mean salary less than
?$61 comma 500
.
This is not an unusual event.
D.
Only
69
?%
of samples of
35
specialists will have a mean salary less than
?$61 comma 500
.
This is an
unusual
event.
Explanation / Answer
mu= 64000
n= 35
sigma= 6000
X= 61500
Z=(X-mu)*sqrt(n)/sigma
=(61500-64000)*sqrt(35)/6000
-2.4650
probability =P(Z<-2.4650)
= 0.006850027
in percentage=100*0.00685=0.685 %
rounded percentage =0.69 %
it is unusual as Z score is more the 2 standard deviation from the mean.
.....................................
A.) Only 0.69 % of samples of 35 specialists will have a mean salary less than $61500 .This is an unusual event.
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