I. Solve for Z and find its area 1. Mean = 81, score: x = 71.5, standard deviation: σ = 9. 2. Mean = 47, score: x = 55.6, standard deviation: σ = 4. 3. Mean = 68, score: x = 78.8, standard deviation: σ = 6.
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.
I. Solve for Z and find its area
1. Mean = 81, score: x = 71.5, standard deviation: σ = 9.
2. Mean = 47, score: x = 55.6, standard deviation: σ = 4.
3. Mean = 68, score: x = 78.8, standard deviation: σ = 6.
4. Mean = 51, score: x = 69, standard deviation: σ =7.
5. Mean = 85, score: x = 93, standard deviation: σ =5.
6. The mean expenses of Dela Cruz Family is PhP12,600 every 15 days and the
standard deviation is PhP 1, 570., If the expenses are
the probability of consuming less than PhP 11,000 in 15 days?
7. The mean production of factory workers is 10 finished products per hour, with a
standard deviation of 1.5 products/hour. What is the probability of finishing: a.
less than 12.8 products/hour? b. more than 12 products/hour?
8. The mean weight of insects for laboratory experiments is 13.2 g, with the standard
deviation of 0.8 g. What is the probability of randomly selecting insects with
weight of : a. 14 g? b. 13.1 to 13.6 g?
9. The lifetime of CP batteries from a certain manufacturer is 25 hours if used
continuously, the standard deviation is 5 hrs. If the distribution is normally
distributed, how many hours is the cut-off in selecting the best 10% in terms of
lifetime?
10. The company’s profit follows a normal distribution with a mean of PhP 500
thousands a month, with a standard deviation of PhP 50 thousands. What is the
lowest 20% of the profit?
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