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.
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.
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.
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.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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