The average number of calories in a 1.5 ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with standard deviation =10. Find the probability that a randomly selected chocolate bar will have
a) Between 200 and 220 calories
b) Less than 200 calories
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The average number of calories in a 1.5 ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with standard deviation =10. Find the probability that a randomly selected chocolate bar will have
a) Between 200 and 220 calories
b) Less than 200 calories
3023
To find the probability that a randomly selected chocolate bar will have a certain number of calories, we need to use the standard normal distribution and convert our values into z-scores.
The z-score formula is:
z = (x - μ) / σ
Where:
- x is the value we want to find the probability for
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
For part (a), the range is between 200 and 220 calories.
To find the probability, we need to calculate the area under the curve between those two values.
Step 1: Convert 200 to a z-score:
z1 = (200 - μ) / σ
Step 2: Convert 220 to a z-score:
z2 = (220 - μ) / σ
Step 3: Use a standard normal distribution table or a calculator to find the probability associated with each z-score.
For part (b), we need to find the probability that a randomly selected chocolate bar will have fewer than 200 calories.
Step 1: Convert 200 to a z-score:
z = (200 - μ) / σ
Step 2: Use a standard normal distribution table or a calculator to find the probability associated with this z-score.
By following these steps, we can find the probabilities for both parts (a) and (b) based on the given mean and standard deviation of the distribution.