Answer:
(0.4958, 0.7422)
Step-by-step explanation:
Let p be the true proportion of water specimens that contain detectable levels of lead. The point estimate for p is . The estimated standard deviation is given by
. Because we have a large sample, the 90% confidence interval for p is given by
where
is the value that satisfies that above this and under the standard normal density there is an area of 0.05. So, the confidence interval is
, i.e., (0.4958, 0.7422).
Answer:
The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
Let <em>p</em> = the proportion of keypads that pass inspection at a cell phone assembly plant.
The probability that a randomly selected cell phone keypad passes the inspection is, <em>p</em> = 0.77.
A random sample of <em>n</em> = 111 keypads is analyzed.
Then the sampling distribution of is:
Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:
Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.