1- A candy maker produces mints that have a label weight of 20.4 grams. Assume t
ID: 3134665 • Letter: 1
Question
1- A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is N(21.37, 0.16). Suppose that 15 mints are independently selected and weighed. Find the probability that at most two of these mints weigh less than 20.857 grams. Hint: You will have to use two different distributions to solve this problem!
2- A radar unit is used to measure the speed of automobiles on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a mean of 62 mph. Find the standard deviation of all speeds if 3% of the automobiles travel faster than 72 mph.
Explanation / Answer
1.
Hi! I am assumig that you use the convention N(u, sigma^2). If you use another convention, please resubmit this question together with the defintion of the symbol N(___, ___). That way we can continue helping you! Thanks!
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 20.857
u = mean = 21.37
s = standard deviation = 0.4
Thus,
z = (x - u) / s = -1.2825
Thus, using a table/technology, the left tailed area of this is
P(z < -1.2825 ) = 0.099833652
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 15
p = the probability of a success = 0.099833652
x = the maximum number of successes = 2
Then the cumulative probability is
P(at most 2 ) = 0.816579873 [ANSWER]
*******************************************
Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.