Solution :
a). This histogram is not a bell shaped.
Here we cannot use the theorem of the central limit as the histogram is being plotted by using 365 samples data values of the one sample.
b). This histogram may be bell shaped approximately since the sample size is large.
Here there are 50 sample each having a size of 500 and there is 50 sample proportions. The histogram shows sampling distribution of the sample proportion. Thus the central limit theorem can be used.
The histogram is approximately bell shaped as there is 50 samples of each having 500 size and an average of 50. Thus the central limit theorem can be used.
c). The histogram is not a bell shaped.
In this case central limit theorem cannot be used as the histogram is plotted by using 100 sample data values of one sample.
d). The histogram is a bell shaped since the sample size is large.
In this case 200 samples of each having a size of 50 and a data values of 50. The histogram here shows a sampling distribution of the sample proportion. Thus the central limit theorem can be used.
In the second also the histogram is of bell shaped as the sample size is large.
There are 200 samples of each sample having a size of 40 and they have 40 data values , i.e. sum of rolls.
e). It is not a bell shaped.
The histogram here is plotted using 100 sample data values having one sample. Therefore we cannot use the central limit theorem.
