Part A of question 1 please. 1. Probability Experiment:a. Construct a probability distribution for the sums shown on the top faces when two dice are rolled. (Hint: X can be 2,3,4,.,12.) You might want to look at Example 4-1 on page 187 and then Figure 4-1on page 187 to help you find the theoretical probabilities of X. Using the probability distribution you constructed, find the mean number of spots.b. Roll two dice 40 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for the sums of your 40 rolls. Using the probability distribution youconstructed, find the mean number of "spots" from your 40 rolls. (If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Placethe pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers 40 different times.)c. Is the mean in (b) close to the mean in (a)? Explain why there is a difference in the two means or why they are the same.Turn in:Sheet with probability distribution and mean for question (a); raw data for 40 sums, probability distribution, and mean for question (b); and answers for question (c). Show work for findingmeans in (a) and (b).2. Normal Problem (Use info in Section 6-3.)Engineers must consider the widths of peoples' heads when designing face masks. Suppose men have head widths that are normally distributed with a mean of 6.125 inches and a standard deviation of1.03 inches.a. If one male is randomly selected, find the probability that his head breadth is less than 6.5 inches.b. If a random sample of 25 males is selected, find the probability that the mean of their head breadths is less than 6.5 inches.c. Is there a difference in the two answers? Explain your answer statistically.Turn in:Sheet with answers for (a), (b), (c) showing work for (a), (b).3. Confidence interval and inference problems (Use formulas given in Chapter 7)Write a confidence interval, showing work, and a statement describing the inference made for each problem:a. For a Statistics course, students are known to have to study daily in order to do well. Data was collected for a sample of 35 stats students from the course and they were found to study for stats for amean of 45 minutes a day. The standard deviation for all the stats students was known to be 5.4. Find a 95% confidence interval for the mean number of minutes that all the stats students study perday.b. A new kind of Covid vaccine is being developed by a medical research team. To test the variability of the new vaccine, a random sample of 16 people were given the new vaccine. Regular blood testsshowed that the sample standard deviation of protection times was 4.7 months. Find a 90% confidence interval for the population standard deviation protection time for the new vaccine.c. A local Dallas basketball legend was known to make a lot of donations to nearby charities. A sample of 30 of his donations had a mean of $41,000 with a standard deviation of $410. Using thissample, find a 99% confidence interval for the mean donation amount for all of his donations.Turn in:Sheet with confidence intervals, including work, and inference statements for the 3 problems. Show work for finding confidence intervals.4. Confidence Interval with Sampling:MacBook Air80DIIDDFIF2F3F4F5F7F8F9F10F11F12@#$&1234589deleteQWERY{}+ II* 00ト※口

A discrete random variable is a variable whose values can be obtained by counting. Though, the…

1. Probability Experiment: a. Construct a probability distribution for the sums shown on the top faces when two dice are rolled. (Hint: X can be 2,3,4,., 12.) You might want to look at Example 4-1 on page 187 and then Figure 4-1 on page 187 to help you find the theoretical probabilities of X. Using the probability distribution you consu distribution for the sums of vour 40 rolls IIsing the prohahility distribution vou n Boll tuo dinn 10 timon ond ror u constructed, find the mean number of spots. O Opote on the ton focos as vou roli Then construct a proha

1. Probability Experiment: a. Construct a probability distribution for the sums shown on the top faces when two dice are rolled. (Hint: X can be 2,3,4,., 12.) You might want to look at Example 4-1 on page 187 and then Figure 4-1 on page 187 to help you find the theoretical probabilities of X. Using the probability distribution you consu distribution for the sums of vour 40 rolls IIsing the prohahility distribution vou n Boll tuo dinn 10 timon ond ror u constructed, find the mean number of spots. O Opote on the ton focos as vou roli Then construct a proha

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q: Part B please

Question

Part A of question 1 please.

1. Probability Experiment:
a. Construct a probability distribution for the sums shown on the top faces when two dice are rolled. (Hint: X can be 2,3,4,.,12.) You might want to look at Example 4-1 on page 187 and then Figure 4-1
on page 187 to help you find the theoretical probabilities of X. Using the probability distribution you constructed, find the mean number of spots.
b. Roll two dice 40 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for the sums of your 40 rolls. Using the probability distribution you
constructed, find the mean number of "spots" from your 40 rolls. (If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Place
the pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers 40 different times.)
c. Is the mean in (b) close to the mean in (a)? Explain why there is a difference in the two means or why they are the same.
Turn in:
Sheet with probability distribution and mean for question (a); raw data for 40 sums, probability distribution, and mean for question (b); and answers for question (c). Show work for finding
means in (a) and (b).
2. Normal Problem (Use info in Section 6-3.)
Engineers must consider the widths of peoples' heads when designing face masks. Suppose men have head widths that are normally distributed with a mean of 6.125 inches and a standard deviation of
1.03 inches.
a. If one male is randomly selected, find the probability that his head breadth is less than 6.5 inches.
b. If a random sample of 25 males is selected, find the probability that the mean of their head breadths is less than 6.5 inches.
c. Is there a difference in the two answers? Explain your answer statistically.
Turn in:
Sheet with answers for (a), (b), (c) showing work for (a), (b).
3. Confidence interval and inference problems (Use formulas given in Chapter 7)
Write a confidence interval, showing work, and a statement describing the inference made for each problem:
a. For a Statistics course, students are known to have to study daily in order to do well. Data was collected for a sample of 35 stats students from the course and they were found to study for stats for a
mean of 45 minutes a day. The standard deviation for all the stats students was known to be 5.4. Find a 95% confidence interval for the mean number of minutes that all the stats students study per
day.
b. A new kind of Covid vaccine is being developed by a medical research team. To test the variability of the new vaccine, a random sample of 16 people were given the new vaccine. Regular blood tests
showed that the sample standard deviation of protection times was 4.7 months. Find a 90% confidence interval for the population standard deviation protection time for the new vaccine.
c. A local Dallas basketball legend was known to make a lot of donations to nearby charities. A sample of 30 of his donations had a mean of $41,000 with a standard deviation of $410. Using this
sample, find a 99% confidence interval for the mean donation amount for all of his donations.
Turn in:
Sheet with confidence intervals, including work, and inference statements for the 3 problems. Show work for finding confidence intervals.
4. Confidence Interval with Sampling:
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