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1) A normal distribution of scores has a variance of S squared = 100. Find the z-scores corresponding to each of the following values:
a) a score that is 20 points above the mean
b) a score that is 10 points below the mean
c) a score that is 15 points above the mean
d) a score that is 30 points below the mean
e) a score that is 5 points above the mean
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2) Given a mean score of 43 and a standard deviation of 5 for teaching readiness test among a sample of students calculate raw scores for the following:
a) a z-score of 1.50
b) a z-score of -2.00
c) a z-score of-.1.20
d) a z-score of 1.30
e) a z-score of -0.80
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3) Subjective wellbeing was measured among a sample of Statistics students with M=150 and S squared=25. Determine the z-scores for the students who obtained the following scores on the subjective wellbeing measure.
a) 110
b) 135
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11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.
For each of the following questions, construct a normal distribution curve and provide the answer.
a) About what percent of the products last between 87 and 93 days?
b) About what percent of the products last 84 or less days?
For each of the following questions, use the standard normal table and provide the answer.
c) About what percent of the products last between 89 and 94 days?
d) About what percent of the products last 95 or more days?
For the periods 2014 to 2019, ESKOM’s electricity percentage price adjustments are given in the
following table:
2014/15 2015/16 2016/17 2017/18 2018/19
7.05% 31.70% 8.18% 1.62% 2.82%
Table 1: Average percentage price adjustments
a) Find the Average (arithmetic mean) percentage price adjustment from
2014 to 2019 (5
Let X be a random variable . P(X=-2)=P(X=-1),P(X=2)=P(X=1),P(X=0)=P(X>0)=P(X<0) . obtain the probability mass function of X
The average price of 350 cellphones is ₱13,500 with the sample standard deviation of ₱750.
a. Find the 99% confidence interval of the true average price of the cellphones.
b. Find the length of the confidence interval.
A researcher wants to estimate the average number of children with congenital heart disease who are between the ages of 1-5 years old. How many children should be enrolled in this study, if the researcher plan on using a 95% confidence level and wants a margin of error of 0.5 and standard deviation 4?
A set of cards contains four suits. Two suits are red, and two suits are black. In each suit there are cards numbered from 2 to 10 as well as a jack, a queen, a king, and an ace. Consider the following probability for one card selected at random.
P(the selected card is a three or a red card)
Suppose that the time required to complete a 1040R tax form is normally distributed with a mean of 100 minutes and a standard deviation of 20 minutes. What proportion of 1040R tax forms will be completed in more than 127 minutes? Round your answer to at least four decimal places.
At a large firm, there is a movement to form a union. Approximately 50% of the entire firm favour unionising, while 30% do not favour unionising. A pro-union leader takes a random sample of 100 workers. Let p1 denote the proportion in this sample that favours a union. An antiunion leader takes an independent random sample of 100 workers. Let p2 denote the proportion in this sample that favours the union. Calculate the probability that p1 exceeds p2 by 0.1 or more. (b) The mean annual income of statisticians of firm 1 is K10, 000 higher than the mean annual income of statisticians of a second firm. Random samples of size n1 = 100 and n2 = 200, respectively, are taken from the two firms. (i) What is the probability that in the two samples the mean annual incomes differ by more than K15, 000? For each firm (population), the standard deviation is K30, 000.
At a large firm, there is a movement to form a union. Approximately 50% of the entire firm favour unionising, while 30% do not favour unionising. A pro-union leader takes a random sample of 100 workers. Let p1 denote the proportion in this sample that favours a union. An antiunion leader takes an independent random sample of 100 workers. Let p2 denote the proportion in this sample that favours the union. Calculate the probability that p1 exceeds p2 by 0.1 or more. (b) The mean annual income of statisticians of firm 1 is K10, 000 higher than the mean annual income of statisticians of a second firm. Random samples of size n1 = 100 and n2 = 200, respectively, are taken from the two firms. (i) What is the probability that in the two samples the mean annual incomes differ by more than K15, 000? For each firm (population), the standard deviation is K30, 000
