X2 + 24x + 141.5 = 0
1 answer:
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Answer:
0.018 is the required probability.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 60,000 miles
Standard Deviation, σ = 1500 miles
We are given that the distribution of tread life is a bell shaped distribution that is a normal distribution.
Formula:
P(brand will last between 56,850 miles and 57,300 miles)
0.018 is the probability a certain tire of this brand will last between 56,850 miles and 57,300 miles.
Answer:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
Let Y the random variable that represent the lenght of time for one individual to be served at the cafeteria. We know from the probalem that
On this case the probability density function would be given by:
And 0 for other case. In order to solve this problem we need to fidn first the probability that a person would be served in less than 2 minutes. And in order to find it we need to find the cumulative distribution function integrating the density function like this:
And with this probability we can find the probability that a person would be served in less than 2 minutes on at least 5 of the next 7 days.
And on this case we can use the binomial distribution, and we want this probability:
We can find the individual probabilities like this: