The amount of algae in a bloom, P, can be modeled by the equation P = t^4 + 6t^3+ 7t^2 + 8t, where t is measured in weeks. Durin
g what interval of t will the population of algae be greater than 500?
(−∞, −6.759) ∪ (3.452, ∞)
(6.759, 3.452)
(0.3452, ∞)
(0, 3.452)
(−∞, −6.759) ∪ (3.452, ∞)
(6.759, 3.452)
(0.3452, ∞)
(0, 3.452)
2 answers:
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Answer: see proof below
<u>Step-by-step explanation:</u>
We have been given that the distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 6. We are asked to find the approximate percentage of lightbulb replacement requests numbering between 38 and 56.
First of all, we will find z-score corresponding to 38 and 56.
Now we will find z-score corresponding to 56.
We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is .
We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.
We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.
Therefore, approximately of lightbulb replacement requests numbering between 38 and 56.