A study has shown that among people without any preschool education, 32% were employed at age 19. If 100 people without preschool education are selected, find the probability that 40 or fewer are employed.
Find z.
z = (x - mean)sd
mean = np
sd = √npq
n = 100
p = .32
q = 1 - p = .68
Substitute 40 for x in the formula. Calculate mean and standard deviation. Plug in the other values. Find z, then check z-table for your probability.
I hope this will help get you started.
To find the probability that 40 or fewer people without preschool education are employed, we need to use the binomial probability formula. The binomial probability formula is given by:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of getting exactly k successes,
n is the number of trials,
k is the number of successes,
p is the probability of success on a single trial, and
( n C k ) is the number of combinations of n items taken k at a time.
In this case, the number of trials is 100 (as 100 people without preschool education are selected), the probability of success (being employed) on a single trial is 0.32 (as 32% were employed), and we want to find the probability of 40 or fewer successes (people employed), so k = 0, 1, 2, ..., 40.
Now let's calculate the probability using this information.
P(40 or fewer people are employed) = P(X ≤ 40) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 40)
To calculate each individual probability, we substitute the values into the binomial probability formula and sum them up:
P(X ≤ 40) = (100 C 0) * 0.32^0 * (1 - 0.32)^(100 - 0) + (100 C 1) * 0.32^1 * (1 - 0.32)^(100 - 1) + ... + (100 C 40) * 0.32^40 * (1 - 0.32)^(100 - 40)
Now we can use a calculator or statistical software to calculate this sum.