You intend to estimate a population proportion with a confidence interval. the data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
while it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 85.8%.
(report answer accurate to three decimal places with appropriate rounding.)
to find the 80th percentile, you have to use one of the inverse cdf functions. norm.dist is not one of them; it returns a probability. the 80th percentile the value of the random variable for which 80% of the distributions falls below that value.
norm.inv(0.80, 475, 33) returns what you want.
norm.s.inv could also work, but not with the given arguments. norm.s.inv(0.80) alone will give you the 80th percentile for the standard normal distribution (mean 0, standard deviation 1), approximately 0.8416. from here, you would convert this value to the given distribution using
norm.inv gives this value directly.
the given expression is
we factor 3 to obtain;
we split the middle term to obtain;
we factor further to get;
we have to move the graph 3 units up.
the equation of the new graph is
y = x^3 + 3