### Problem Statement**CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the standard deviation is 252 dollars, and the cost is normally distributed. You take a simple random sample of 39 auto insurance policies. Round your answers to 4 decimal places.**#### Questions:1. **What is the distribution of $ X $?** $ X \sim N(\hspace{50px}, \hspace{50px}) $2. **What is the distribution of $ \overline{X} $?** $ \overline{X} \sim N(\hspace{50px}, \hspace{50px}) $3. **What is the probability that one randomly selected auto insurance is more than $1028?** $\hspace{300px}$4. **A simple random sample of 39 auto insurance policies, find the probability that the average cost is more than $1028.** $\hspace{300px}$5. **For part d), is the assumption of normal necessary?** - $ \bigcirc $ Yes - $ \bigcirc $ No### Graphs or Diagrams:There are no graphs or diagrams in the image. The image consists purely of textual statistical problems that pertain to the distribution and probability calculations involving the normal distribution.### Explanation:1. The blank spaces in parts (a) and (b) are meant to be filled in with the parameters of the normal distribution for $ X $ and $ \overline{X} $, respectively.2. For part (c), the box is intended for the calculation of the probability.3. For part (d), the box is intended for the probability calculation of the average cost being more than $1028.4. Part (e) asks the reader to consider whether assuming normality is necessary to solve part (d).This structure left by the several questions would guide students through calculations involving standard normal distributions and their applications in problem-solving.

Since there are multiple sub-parts, as per the honor code the first three sub-parts will be solved.…

Answered: CNNBC recently reported that the mean…

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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CNNBC recently reported that the mean annual cost of auto insurance is 1017 dollars. Assume the standard deviation is 249 dollars, and the cost is normally distributed. You take a simple random sample of 37 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( b. What is the distribution of a? ¤ - N( c. What is the probability that one randomly selected auto insurance is less than $997? d. a simple random sample of 37 auto insurance policies, find the probability that the average cost is less than $997.
Private nonprofit four-year colleges charge, on average, $27,088 per year in tuition and fees. The standard deviation is $7,205. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 26,156 per year. c. Find the 60th percentile for this distribution. S (Round to the nearest dollar.)
Private nonprofit four-year colleges charge, on average, $26,521 per year in tuition and fees. The standard deviation is $7,011. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 24,703 per year. c. Find the 70th percentile for this distribution. $ (Round to the nearest dollar.)
Many college admissions want to know your class percentage in addition to your grades. The grades are normally distributed. A certain university insists that a student place in at the 90th percentile. if the mean is 79.45 and the standard deviation is 5.37, what is the 90th percentile? a.88.07 b.85.01 c.86.33 d.90
QUEST A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. The top 15% of the students taking the test scored will receive a grade of B. What is the cur score?
Use the normal distribution of SAT critical reading scores for which the mean is 514 and the standard deviation is 115. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 650? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? Click to view page 1 of the standard normal table. LOADING... Click to view page 2 of the standard normal table. LOADING... Question content area bottom Part 1 (a) Approximately 1.181.18% of the SAT verbal scores are less than 650. (Round to two decimal places as needed.) Part 2 (b) You would expect that approximately 0.880.88 SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.)
Please answer B, C, & D.
Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births. Click the icon to view the data table. The mean is u= girl(s). (Round to one decimal place as needed.) The standard deviation is o = e# girl(s). (Round to one decimal place as needed.) Table of numbers of girls and probabilities Number of Girls x 0 1 2 3 4 5 6 7 8 átv P(x) 0.004 0.034 0.117 0.218 0.278 0.217 0.102 0.027 0.003 D - X NiZ Next
Private nonprofit four-year colleges charge, on average, $26,375 per year in tuition and fees. The standard deviation is $6,685. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 24,855 per year. c. Find the 80th percentile for this distribution. $ (Round to the nearest dollar.)
Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $181,000. Assume the standard deviation is $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N b. What is the distribution of a? - NO c. For a single randomly selected graduate, find the probability that her salary is between $180,714 and $188,276. d. For a simple random sample of 39 graduates, find the probability that the average salary is between $180,714 and $188,276. e. For part d), is the assumption of normal necessary? O No Yes Question Help: Message instructor Submit Question
A successful basketball player has a height of 6 feet 11 inches, or 211 cm. Based on statistics from a data set, his height converts to the z score of 5.17. How many standard deviations is his height above the mean?
Private nonprofit four-year colleges charge, on average, $26,168 per year in tuition and fees. The standard deviation is $6,656. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 24,347 per year. c. Find the 74th percentile for this distribution. $ (Round to the nearest dollar.)

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