Suppose that people’s weights are normally distributed, with mean 175 pounds and a standard deviation of 6 pounds. Round to the nearest hundredth of a percent
a. What percent of the population would weigh between 165 and 170 pounds?
b. What percent of the population would you expect to weigh more than 182 pounds?
c. What percent of the population would you expect to weigh between 172 and 180 pounds?
d. What percent of the population would you expect to be heavier than 163 pounds?
the worksheet is titles the normal curve, im not sure how to figure the percent out
your magic webpage for this stuff
http://davidmlane.com/hyperstat/z_table.html
i used this page for these answers and they came up all wrong, i don't understand how to use the information given to calculate the percent
To calculate the percentages for each scenario, we will use the concept of the normal distribution and the standardized z-score.
a. To find the percentage of the population that weighs between 165 and 170 pounds, we need to find the area under the normal curve between these two values.
1. First, we need to convert each weight into a standardized z-score using the formula: z = (x - mean) / standard deviation.
For 165 pounds: z1 = (165 - 175) / 6 = -1.67
For 170 pounds: z2 = (170 - 175) / 6 = -0.83
2. Next, we need to find the area between these two z-scores using a standard normal distribution table or statistical software. If you're using a standard normal distribution table, find the area corresponding to z1 and z2 separately. Then find the difference between these two values to get the desired percentage.
b. To find the percentage of the population that would weigh more than 182 pounds, we need to find the area to the right of 182 pounds on the normal curve.
1. Convert the weight of 182 pounds into a standardized z-score using the formula: z = (x - mean) / standard deviation.
For 182 pounds: z = (182 - 175) / 6 = 1.17
2. Find the area to the right of this z-score using a standard normal distribution table or statistical software.
c. To find the percentage of the population that would weigh between 172 and 180 pounds, we again need to find the area under the normal curve between these two values.
1. Convert each weight into a standardized z-score using the formula: z = (x - mean) / standard deviation.
For 172 pounds: z1 = (172 - 175) / 6 = -0.5
For 180 pounds: z2 = (180 - 175) / 6 = 0.83
2. Find the area between these two z-scores using a standard normal distribution table or statistical software.
d. To find the percentage of the population that would be heavier than 163 pounds, we need to find the area to the right of 163 pounds on the normal curve.
1. Convert the weight of 163 pounds into a standardized z-score using the formula: z = (x - mean) / standard deviation.
For 163 pounds: z = (163 - 175) / 6 = -2
2. Find the area to the right of this z-score using a standard normal distribution table or statistical software.
Remember to round the percentages to the nearest hundredth of a percent as requested.