Please help, I don't know how to do this and need it done quickly, thanks for your help and time! have a good day :)
1 answer:
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Answer: The probability that exactly 2 insects will survive = 0.2501
Step-by-step explanation:
Given: A certain insecticide kills 80% of all insects in laboratory experiments.
The probability that a particular insect survives= 1-0.80=0.20
Sample size: n=14
Binomial probability distribution:
, where x= number of successes , p=probability of success in each trial, n= sample size.
The probability that exactly 2 insects will survive =
Hence, the probability that exactly 2 insects will survive = 0.2501
Using the z-distribution, it is found that the smallest sample size required is given by:
B) 7 vehicles.
<h3>What is the margin of error for a z-distribution confidence interval?</h3>It is given by:
In which:
- z is the critical value.
is the population standard deviation.
- n is the sample size.
In this problem, we have a 90% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
The margin of error and the population standard deviation are given by, respectively:
.
Then, we solve for n to find the needed sample size.
Rounding up, 7 vehicles have to be sampled, hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/25890103