I need some help understanding this and demonstrating how to work through them w
ID: 3294170 • Letter: I
Question
I need some help understanding this and demonstrating how to work through them would be nice
1. Assume it is known from past studies that 40% of people that get mail-order catalogs order something from the catalog.
(a) If a catalog is sent to 100 people, what is the probability that exactly 20 of them will order something from the catalog?
(b) If a catalog is sent to 10 people, what is the probability that at least one person orders something from the catalog?
2. Assume IQ scores are normally distributed; with a mean of 100 and a standard deviation of about 15.
(a) What percentage of the population can be expected to have IQ scores lying in the range from 88 to 112?
(b) What proportion of people have IQ scores about 130?
(c) What IQ score must a person obtain in an IQ in order to belong to the top 5 percent?
3. A tire company find that the lifespan for one brand of its tires is normally distributed with a mean of 47500 miles and a standard deviation of 3000 miles. If the manufacturer is willing to replace no more than 10% of its tires, what should be the approximate number of miles for a warranty?
4. A wine bottler has two machines for cutting corks for use in wine bottles. The first produces corks with normally distributed diameters of mean 3 cm and standard deviation 0.1 cm. The second machine produces corks whose diameters are normally distributed with mean 3.04 cm and standard deviation 0.02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. Which machine produces a higher percentage of acceptable corks?
Explanation / Answer
Solution:-
1)
p = 40/100
p = 0.40
(a) The probability that exactly 20 of them will order something from the catalog is 0.0000105.
n = 100, x = 20
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(x = 20) = 0.0000105
(b) The probability that at least one person orders something from the catalog is 0.994.
n = 10, x = 1
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(x > 1) = 0.994