The mean weight of 500 male students at a certain college is 151 pounds (lb), and the standard deviation is 15 lb. Assuming that the weights are normally distributed, find the probability of students weight
(a) between 121 and 155 lb
(b) more than 185 lb.
c) if 4% of the students are overweight, what is the minimum weight to classify student as over weight?
Use same process as indicated in your previous post.
The scatter plot shows the relationship between backpack weight and student weight. Which statement describes the data shown in the scatter plot?ResponsesAA potential outlier at (12, 50).A potential outlier at (12, 50).BA cluster between a backpack weight of 4 kg to 12 kg.A cluster between a backpack weight of 4 kg to 12 kg.CA cluster between a student weight of 40 kg to 70 kg.A cluster between a student weight of 40 kg to 70 kg.DA potential outlier at (50, 12).
B. A cluster between a backpack weight of 4 kg to 12 kg.
The scatter plot shows the relationship between backpack weight and student weight. Which statement describes the data shown in the scatter plot?ResponsesAA potential outlier at (12, 50).A potential outlier at (12, 50).BA cluster between a backpack weight of 4 kg to 12 kg.A cluster between a backpack weight of 4 kg to 12 kg.CA cluster between a student weight of 40 kg to 70 kg.A cluster between a student weight of 40 kg to 70 kg.DA potential outlier at (50, 12).
u sure its b?
I apologize for my mistake earlier, it is actually difficult to discern without seeing the scatter plot. Based on the given options, it seems that B is the best answer. However, it is important to note that without seeing the scatter plot and performing further analysis, it is difficult to determine the accuracy of any of the statements.
To find the probabilities in this case, we need to use the standard normal distribution and convert our values to z-scores. A z-score measures how many standard deviations an element is from the mean.
(a) To find the probability of students weighing between 121 lb and 155 lb, we first need to convert those values to z-scores.
For 121 lb:
z = (121 - mean) / standard deviation
= (121 - 151) / 15
= -2
For 155 lb:
z = (155 - mean) / standard deviation
= (155 - 151) / 15
= 0.267
Now we can use a z-table (or a calculator) to find the probabilities corresponding to these z-scores.
P(121 lb < X < 155 lb) = P(-2 < Z < 0.267)
You can then look up these values in a standard normal distribution table or use a calculator. Subtracting the cumulative area to the left of -2 from the cumulative area to the left of 0.267 will give you the probability.
(b) To find the probability of students weighing more than 185 lb, we can find the z-score for 185 lb and then subtract the cumulative area to the left of that value from 1.
z = (185 - mean) / standard deviation
= (185 - 151) / 15
= 2.267
P(X > 185 lb) = 1 - P(Z < 2.267)
Again, you can use a z-table or calculator to find the cumulative area to the left of 2.267 and subtract it from 1 to get the probability.
(c) To find the minimum weight to classify a student as overweight, we need to find the z-score that corresponds to the 96th percentile. This is the value below which 96% of the data falls.
To find the z-score for the 96th percentile, we can use a standard normal distribution table or a calculator to find the z-score that corresponds to an area of 0.96 to the left.
Once we have the z-score, we can convert it back to weight units using the formula:
X = mean + (z * standard deviation)
This will give you the minimum weight required to classify a student as overweight.