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The life of a certain type of automobile tire is normally distributed with mean 34,000 miles and standard deviation 4000 miles. a. What is the probability that such a tire lasts over 40,000 miles? b. What is the probability that it lasts between 30,000 and 35,000 miles? c. Given that it has survived 30,000 miles, what is the conditional probability that it survives another 10,000 miles?
A hospital keeps records of its emergency-room traffic. Those records indicate that, beginning at 6:00 P.M. on any given day, the elapsed time until the first patient arrives has an exponential distribution with parameter λ = 6.9, where time is measured in hours. Determine the probability that, beginning at 6:00 P.M. on any given day, the first patient arrives
a. between 6:15 P.M. and 6:30 P.M.
b. before 7:00 P.M.
c. given that the first patient doesn’t arrive by 6:15 P.M., determine the probability that she arrives by 6:45 P.M.
Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17. Carlos has two more 20-point homework assignments to complete before his progress report gets sent out, and he wanted to raise his mean score to an 18. Is it possible for Carlos to raise his score to an 18?
A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 6000 hours and a standard deviation of 400 hours. A random sample of 16 bulbs had an average life of 5850 hours. If the manufacturer’s claim is correct-
a. What is the sampling distribution of the sample mean?
b. what is the probability of finding a sample mean of 5850 or less?
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 270 vinyl gloves, 59% leaked viruses. Among 270 latex gloves, 12% leaked viruses. Using the accompanying display of the technology results, and using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population
what are the null and alternative hypotheses?
identify the test statistic?
identify p-value?
conclusion?
Solve the following by applying the concepts of percentiles under the normal curve. Show complete solution and draw the normal curve.
1.In a National Achievement Test, the mean was found to be 75 and the standard deviation was 15. The scores also approximate the normal distribution.
a. What is the minimum score that belongs to the upper 15% of the group? (w/ illustration)
b. What is the two extreme scores outside of which 15% of the group are expected to fall?(w/ illustration)
c. What is the score that divide the distribution into two such that 75% of the cases below it?(w/ illustration)
d. Estimate the range of scores that will include the middle 45% of the distribution. (w/ illustration)
2.Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100.
a. What is the minimum score necessary to be in the top 15% of the SAT distribution?
b. Find the range of scores that defines the middle 80% of the distribution of SAT scores.
Show complete solutions for each item.
Locate the following percentile under the normal curve
Find the nearest area and the z-score.
Percentile
a. 𝑃76
b. 𝑃54
c. 𝑃34
d. 𝑃25
e. 𝑃94
f. 𝑃89
g. 𝑃90
h. 𝑃68
i. 𝑃15
j. 𝑃42
Q2. Estimate kurtosis.
X Frequency
1 – 5 12
5 – 10 11
10 – 15 10
15 – 20 4
20 – 25 3
Q1. Define kurtosis. If β1=1 and β2 =4 and variance = 9, find the values of β3 and β4 and comment upon the nature of the distribution.
It has been reported that 70% of university students do volunteer work during their summer vacation. Four students are randomly selected to do volunteer work.
a. The probability that at least 1 student will do volunteer work this summer (correct to 3 decimal places) is
b. The probability that exactly 3 graduates will not do any volunteer work this summer (correct to 4 decimal places) is
c. The expected number of students (correct to 1 decimal place) who will not do volunteer work this summer is
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#340153 on Dec 2023