Find the mean, [tex]$\mu$[/tex], for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
[tex]$n=625 ; p=0.7$[/tex]
Answer (2)
The problem provides a binomial distribution with n = 625 and p = 0.7 .
The formula for the mean of a binomial distribution is μ = n × p .
Substitute the given values into the formula: μ = 625 × 0.7 = 437.5 .
The mean of the binomial distribution is 437.5 .
Explanation
Understand the problem and provided data We are given a binomial distribution with parameters n = 625 and p = 0.7 . We need to find the mean, μ , of this binomial distribution and round the answer to the nearest tenth.
Recall the formula for the mean of a binomial distribution The mean of a binomial distribution is given by the formula μ = n p , where n is the number of trials and p is the probability of success in each trial.
Substitute the values of n and p Substitute the given values of n and p into the formula: μ = 625 × 0.7
Calculate the mean Calculate the value of μ : μ = 437.5
State the final answer Since the result is already given to the nearest tenth, no further rounding is needed. The mean of the binomial distribution is 437.5 .
Examples
Consider a scenario where a pharmaceutical company is testing a new drug. They administer the drug to 625 patients ( n = 625 ) and find that the drug is effective in 70% of the patients ( p = 0.7 ). The mean number of patients who experience the drug's effectiveness can be calculated using the binomial distribution's mean formula, μ = n × p . In this case, μ = 625 × 0.7 = 437.5 . This means that, on average, the drug is effective for approximately 437.5 patients out of the 625.
The mean of the binomial distribution with n = 625 and p = 0.7 is calculated using the formula μ = n × p . The result is μ = 437.5 , rounded to the nearest tenth. Therefore, the mean is 437.5 .
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