Answer:
15.87%
Step-by-step explanation:
Given that:
The mean (μ) = 1000 hours, the standard deviation (σ) = 100 hours.
The z score provides a means of measurement in statistics to determine the variation of a raw score from the mean. The z score is given as:
To find that a randomly chosen light bulb will last less than 900 hours:
Therefore, P(x < 900) = P(z < -1) = 0.1587 = 15.87%
Using the Empirical Rule, it is found that:
a) About 68% of organs will be between 325 and 375 grams.
b) 99.7% of organs weighs between 275 grams and 425 grams.
c) 0.3% of organs weighs less than 275 grams or more than 425 grams.
d) 81.5% of organs weighs between 325 grams and 400 grams.
<h3>What is the Empirical Rule?</h3>It states that, for a normally distributed random variable:
In this problem:
Item a:
Within 1 standard deviation of the mean, hence:
350 - 25 = 325.
350 + 25 = 375.
About 68% of organs will be between 325 and 375 grams.
Item b:
Within 75 grams of the mean, hence within 3 standard deviations, so 99.7% of organs weighs between 275 grams and 425 grams.
Item c:
More than 3 standard deviations from the mean, hence 100 - 99.7 = 0.3% of organs weighs less than 275 grams or more than 425 grams.
Item d:
Between 1 standard deviation below the mean and 2 above. Considering the symmetry of the normal distribution:
81.5% of organs weighs between 325 grams and 400 grams.
To learn more about the Empirical Rule, you can take a look at brainly.com/question/24537145
To solve this question we will use the following diagram:
From the diagram, we get that the diameter of the semicircle is 8cm.
The perimeter of the figure is:
Substituting π=3.14 and simplifying we get:
Now, the area of the given figure is the area of the rectangle plus the area of the semicircle:
Substituting π=3.14 and simplifying we get:
Answer:
