Please I need help!
The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 418 jawbreakers that weigh more than .4 ounces?
Well, that depends on your definition of "unusual." If you consider the fact that 60% of jawbreakers produced by the Acme Candy Company weigh more than .4 ounces, then it wouldn't be particularly unusual to have 418 jawbreakers in a sample of 800 that meet this criteria. However, if you were hoping for a different kind of surprise, like finding a golden ticket or a unicorn, then yes, it would be quite unusual indeed!
To determine whether it would be unusual for this sample of 800 to contain 418 jawbreakers that weigh more than .4 ounces, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx)(p^x)(q^(n-x))
Where:
- P(x) is the probability of getting exactly x successes (jawbreakers weighing more than .4 ounces)
- n is the total number of trials (800 jawbreakers)
- x is the number of successful trials (418 jawbreakers weighing more than .4 ounces)
- p is the probability of success on a single trial (60% or 0.6)
- q is the probability of failure on a single trial (40% or 0.4)
Using these values, we can calculate the probability of obtaining exactly 418 jawbreakers weighing more than .4 ounces out of a sample of 800.
P(418) = (800C418)(0.6^418)(0.4^(800-418))
To calculate this, you can use a calculator or statistical software. However, for demonstration purposes, let's use the binomial probability calculator available online.
Entering the values into the calculator, we find that the probability is approximately 0.014, or 1.4%.
Since this probability is relatively small, it would indeed be considered unusual to have exactly 418 jawbreakers that weigh more than .4 ounces in a sample of 800. However, the term "unusual" can be subjective, and it depends on the specific context and criteria for determining what is considered unusual or significant in this scenario.
To determine if it would be unusual for the sample of 800 to contain 418 jawbreakers that weigh more than .4 ounces, we need to compare the observed number of jawbreakers with the expected number.
First, we need to compute the expected number of jawbreakers that weigh more than .4 ounces. Since the Acme Candy Company claims that 60% of the jawbreakers weigh more than .4 ounces, we can expect that 60% of the 800 jawbreakers, or 0.6 * 800 = 480 jawbreakers, will weigh more than .4 ounces.
Now, we need to determine if the observed number of 418 is significantly different from the expected number of 480. To do this, we can use the binomial probability formula to calculate the probability of obtaining 418 or fewer jawbreakers that weigh more than .4 ounces out of the 800 sampled.
P(X ≤ 418) = Σ (800 choose x) * (0.6)^x * (0.4)^(800-x) for x = 0 to 418
We can use statistical software, a binomial probability calculator, or a binomial distribution table to find this probability.
If the probability is very small (e.g., less than 0.05, which is often used as a threshold for significance), then it would be considered unusual to obtain 418 or fewer jawbreakers that weigh more than .4 ounces out of the 800 sampled.