Suppose the actual proportion of USU students who feel parking is a problem is 0.70. A student takes a poll of 100 randomly selected Purdue students and asks them if they feel that parking is a problem.
a. What is the mean
for the sample proportion?
b. What is the standard deviation for the sample proportion? (Use 4
decimals)
c. What is the probability that the sample proportion is greater
than 0.75? (Use 4 decimals)
d. Between what two values does the middle 95% of the sample
proportions lie? (Use 4 decimals)
Given data
population proportion (p) =0.70
number of sample (n)=100
a) mean of the sample proportion
will be same as the sample population proportion
b)Standard deviation for the sample will be
c)now we have to find the probability of that sample proportion is greater than 0.75
So
Now test Statistic
Now from the standard probability distribution table the
probability less than Z=1.09 will be
the probability of getting sample proportion greater than 0.75 will be
d) Since this distribution is a normal distribution so According to empirical rule the 95 % of the sample proportion lies within 2 standard deviation of the mean
that is
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