In October 2024
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the result of a nationwide aptitude test in mathematics are normally distributed with μ 80 and σ 15. what is the score that divides the distribution such that 99% of the cases is below it
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.
a. What is the probability that all six arrive within 2 days?
b. What is the probability that exactly five arrive within 2 days?
c. Find the mean number of letters that will arrive within 2 days.
d. Compute the variance and standard deviation of the number that will arrive within 2 days.
order to estimate the mean amount of damage sustained by vehicleswhen a deer is struck, an insurance company examined the records of 50such occurrences, and obtained a sample mean of $2,785 with sample standard deviation $221. Construct a 95% confidence interval for the mean amount of damage in all such accidents
Activity 2. Construct Me!
A population consists of the five numbers 2, 3, 6, 8 and 11.
Consider samples of size 2 that can be drawn from this population.
a. List all the possible samples and the corresponding mean.
Sample
Mean
19
b. Construct the sampling distribution of the sample means.
Sample Mean
Probability
Frequency
c. Draw a histogram of the sampling distribution of the
meets.
According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? [10] (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? [10]
A dean has found that 62% of entering freshmen and 78% of community college transfers eventually graduate. Of all entering students, 73% are entering freshmen and the remainder are community college transfers. a. What is the probability that a randomly chosen entering student is an entering freshman who will eventually graduate? b. Find the probability that a randomly chosen entering student will eventually graduate. c. What is the probability that a randomly chosen entering student either is an entering freshman or will eventually graduate (or both)? d. Are the events “eventually graduates” and “enters as community college transfer” statistically independent?
The masses of 50 castings were measures. the results in kilograms were as follows: 4.6 4.7 4.5 4.6 4.7 4.4 4.8 4.3 4.2 4.8 4.7 4.5 4.7 4.4 4.5 4.5 4.6 4.4 4.6 4.6 4.8 4.3 4.8 4.5 4.5 4.6 4.6 4.7 4.6 4.7 4.4 4.6 4.5 4.4 4.3 4.7 4.7 4.6 4.6 4.8 4.9 4.4 4.5 4.7 4.4 4.5 4.9 4.7 4.5 4.6 (a) Arrange the data in 8 equal classes between 4.2 and 4.9 kilograms. [5] (b) Determine the frequency distribution for the 8 classes in (a). [5] (c) Draw the frequency histogram and frequency polygon using different colors for the frequency distribution in (b). [10] (d) For each of the 8 classes formed in (a), calculate the central value, the relative frequency, the lower boundary, and the upper boundary. [10] (e) Find the mean, median, mode, and standard deviation for the grouped data in (b). [30]
The Head of the Math Department announced that the mean score of Grade 11 students in St. James High School in the medterm examination in statistics and probability was 88 and the standard deviation was 10. One student who believed that the mean score was less than this, randomly selected 35 students and computed their mean score. She obtained a mean score of 84. At 0.01 level of significance, test the student’s belief.
If scores are normally distributed with the mean of 30 and standard deviation of 5. what percent score is.
given the population mean of 12 and a sample deviation of 3 in a sample size of 125
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#340153 on Dec 2023