QUESTION FOUR (a) During observations on a patch of white dead nettles it was noticed that the numbers of flowers visited by bees during 100 5-minutes intervals were as follows: Number of flowers visited/ 5- minutes interval Frequency 0 – 5 4 6 – 11 8 12 – 17 13 18 – 23 16 24 – 29 22 30 – 35 17 36 – 41 10 42 – 47 6 48 – 53 3 54 – 59 1 5 i. Calculate the mean and variance for the data. ii. Find the expected frequencies for a normal distribution with the same mean and variance. iii. Using the chi-square distribution. Test, at the 5% level of significance, how well the observed data fits this normal distribution.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
QUESTION FOUR
(a) During observations on a patch of white dead nettles it was noticed that the numbers of
flowers visited by bees during 100 5-minutes intervals were as follows:
Number of flowers visited/ 5-
minutes interval
Frequency
0 – 5 4
6 – 11 8
12 – 17 13
18 – 23 16
24 – 29 22
30 – 35 17
36 – 41 10
42 – 47 6
48 – 53 3
54 – 59 1
5
i. Calculate the mean and variance for the data.
ii. Find the expected frequencies for a
variance.
iii. Using the chi-square distribution. Test, at the 5% level of significance, how well
the observed data fits this normal distribution.
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