A group of laboratory animals is infected with a particular form of bacteria, an
ID: 3273683 • Letter: A
Question
A group of laboratory animals is infected with a particular form of bacteria, and their survival time is found to average 38 days, with a standard deviation of 40 days. You can use the Empirical Rule to see why the distribution of survival times could not be mound-shaped. (a) Find the value of x that is exactly one standard deviation below the mean. x = days (b) If the distribution is in fact mound-shaped, approximately what percentage of the measurements should be less than the value of x found in part (a)? % (c) Since the variable being measured is time, is it possible to find any measurements that are more than one standard deviation below the mean? Yes No (d) Use your answers to parts (b) and (c) to explain why the data distribution cannot be mound-shaped. The approximate values given by the Empirical Rule accurate, indicating that the distribution be mound-shaped.
Explanation / Answer
Here we are given that the mean is 38 days and the standard deviation, SD = 40 days
a) The x value that is exactly one standard deviation below the mean is computed as:
mean - SD = 38 - 40 = -2 days
b) By empirical rule 68% of the observations lies within 1 standard deviation from the mean. Therefore 100 - 68 = 32% lies outside one standard deviation of the mean. Due to symmetry 32/2 = 16% lies on either side therefore 16% of the observations must lie below -2 days
c) No it is not possible to do that because the time quantitity cannot be negative and one standard deviaiton below mean is actually negative 2 days
d) The data distribution cannot be mould shaped, because as we saw in part b) that 16% of the observations must lie below -2 days but no observation here lies below 0 as time is the variable here and time cannot be negative. Therefore the given distribution cannot be mould shaped.
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