1.The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.9, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 1.3. (a) What are the mean and standard deviation of the average number of moths x in 75 traps? (Round answers to a maximum of three decimal places.) mean = standard deviation = (b) Use the central limit theorem to find the probability that the average number of moths in 75 traps is greater than 0.6. (Round answer to four decimal places.) 2.Answer the following. In a normal distribution, x = 6 and z = −1.9. This tells you that x = 6 is........... standard deviations to the ---Select--- left right of the mean
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.
1.The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the
| mean | = | |
| standard deviation | = |
(b) Use the central limit theorem to find the probability that the average number of moths in 75 traps is greater than 0.6. (Round answer to four decimal places.)
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