Mark bought a plane ticket for $234, which was 80% of the original price. How much was the original price?
2 answers:
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Answer:
865
Step-by-step explanation:
We have that in 95% confidence level the value of z has a value of 1.96. This can be confirmed in the attached image of the normal distribution.
Now we have the following formula:
n = [z / E] ^ 2 * (p * q)
where n is the sample size, which is what we want to calculate, "E" is the error that is 2% or 0.02. "p" is the probability they give us, 5 out of 50, is the same as 1 out of 10, that is 0.1. "q" is the complement of p, that is, 1 - 0.1 = 0.9, that is, the value of q is 0.9.
Replacing these values we are left with:
n = [1.96 / 0.02] ^ 2 * [(0.1) * (0.9)]
n = 864.36
865 by rounding to the largest number.
Answer:
The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).
Step-by-step explanation:
The formula for estimating the population proportion by a confidence interval is given by:
Where:
is the sample's proportion of success, which in this case is the people that regularly lie during surveys,
is the critical value needed to find the tails of distribution related to the confidence level,
is the sample's size.
<u>First</u> we compute the value:
<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):
Now we can replace in the formula with the obtained values to compute the confidence interval:
