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The average age of community college students is 18.6 years.
Weights of newborn babies in a particular city are normally distributed with a mean of
3360 g and a standard deviation of 450 g.
a.
A newborn weighing less than 2100 g is considered to be at risk because the mortality rate for this group is very low. If a hospital in the city has 900 births in a
year, how many of those babies are in the “at-risk” category?
b.
If we redefine a baby to be at risk if his or her birth weight is in the lowest 1%,
find the weight that becomes the cutoff separating at-risk babies from those who
are not at risk.
c.
If 30 newborn babies are randomly selected as a sample in a study, find the probability that their mean weight is between 3000 g and 3500 g.
The standard deviation of the apples surveyed from a sample of measurements taken from 11 apples is found to be 4.934 grams. Find the 95% confidence intervals for the standard deviation of these weights.
Hydrangea is a flower that changes its color according the the pH of the soil. The flower becomes blue when the pH of the soil is too acidic (pH below 5.5), red when the pH of the soil is too basic (pH above 6.5), and purple when the pH of the soil is exactly between 5.5 to 6.5. A landowner claims that the average pH of their soil can produce perfectly consistent purple flowers with a standard deviation pH of at most 0.5.
A flower cultivator thinks the standard deviation of the pH of the soil may be greater than 0.5, so they tested 15 random sites from the land area. Use a level of significance of α = 0.05.
A builder claims that bidets are installed in more than 50% of all homes being constructed today in suburban Lapu-lapu. Would you agree with this claim if a random survey of new homes in this city showed that 54 out of 150 had bidets installed? Use a 0.05 level of significance.
(a) A fair coin is tossed until a head is obtained. What is the probability that the number of tosses required is an odd number?
(b) A fair die is thrown seven times. Find the probability that the outcome contains one ‘1’, two ‘2’, three ‘3’, but no ‘4’?
I would like to know how to calculate these questions, thanks!
In a production process, a total number of 100 items were produced by machines M1, M2 and M3. Of those items being produced, 37 were made by machine M1, 42 were made by M2, and 21 were made by M3. The three machines work independently, however, they do not work perfectly. From the experience, 5% of the items produced by M1 are defective, 4% of the items produced by M2 are defective, and 3% of the items produced by M3 are defective.
a) Given that a randomly selected item is non-defective, what is the probability that it is produced by machine M1?
(b) If two items which are not produced by machine M3 are selected at random without replacement, what is the probability that at least one of them is non-defective?
Assume that when adults with smartphones are randomly selected,
44% use them in meetings or classes. If
6 adult smartphone users are randomly selected, find the probability that exactly
4 of them use their smartphones in meetings or classes.
Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n=8 trials, each with probability of success (correct) given by p=0.4. Find the indicated probability for the number of correct answers.
