Answer:
The percentage of cockroaches weighing between 77 grams and 83 grams is about 55%.
Explanation:
Given : The weights of cockroaches living in a typical college dormitory are approximately distributed with a mean of 80 grams and a standard deviation of 4 grams.
To find : The percentage of cockroaches weighing between 77 grams and 83 grams is about __% ?
Solution :
Applying z-score formula,

Where, x is the sample mean
is the population mean
is the standard deviation.
For x=77 z-score is



For x=83 z-score is



The probability of z lie between 77 and 83 is given by z-score table,


The weighing between 77 grams and 83 grams is given by,



Converting into percentage,


Round to nearest whole number -

Therefore, The percentage of cockroaches weighing between 77 grams and 83 grams is about 55%.