Example 10.7 In a certain locality, the average rent paid by all tenants amounts to Rs 1,500 pm with astandard deviation of Rs 450. However, the population distribution of rents pertaining to all tenants inthat city is positively skewed. Find out the mean and standard deviation of when the sample size is(a) 30 and (b) 100. Also describe the shape of its sampling distribution in both the cases.

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Answered: Example 10.7 In a certain locality, the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The GSS survey is conducted for approximately 2200 adults every year, since 1972 for a total of more than 38,000 participants. During several years of the GSS, participants were asked how many close friends they have. The mean for this variable was 7.44 friends, with a standard deviation of 10.98. The median was 5.00 and the mode was 4.00. What do the mean and standard deviation suggest about the shape of the distribution?
The scores in a test conducted to 500 students are normally distributed with a mean of 110 and a standard deviation of 6. How may students get a score below 102?
Suppose that the distance of fly balls hit to the outfield is normally distributed with a mean of 252 feet in a standard deviation of 50 feet find the 70th percentile of the distribution of the average of 49 fly balls
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 260 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. -Find the 70th percentile of the distribution of the average of 49 fly balls
National Cookie Company produces premium chocolate chip cookies for sale in up-scale food markets. Cookies are sold in 250 gram packages of 10 cookies. Unfortunately, the manufacturing process has some inherent variation. After years of improving the process, National has reduced the standard deviation of the process to 0.6 grams per cookie. In the short term, the variation of 2 the production process is outside National’s control. However, National is able to adjust the mean weight level for each cookie. For various economic reasons, setting the mean level properly is important. If it is too high, then the cookies are heavier than required and National must incur unnecessarily high raw material costs; if the mean level is too low, then the cookies must be sold as thrift. a) Assume that National sets the maximum number of underweight packages at 2.5%. Where should National set the mean weight level per cookie?
It seems these days that college graduates who are employed full time work more than 40 hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 22 respondents who were college graduates employed full time. The mean number of hours worked per week by these 22 respondents was 43 hours, with a standard deviation of 8 hours. Assume that the population of hours worked per week by college graduates employed full time is normally distributed with mean. Can we conclude that mean is greater than 40 hours? Use the 0.1 level of significance. Perform a one tailed test, and complete the parts below.
It seems these days that college graduates who are employed FT work more than 40-hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 15 respondents who were college graduates employed FT. The mean number of hours worked per week by these 15 respondents was 44 hours, with a standard deviation of 8 hours. Assume that the population of hours worked per week by college graduates employed FT normally distributed with mean u. Can we conclude that u is greater than 40 hours? Use the 0.1 level of significance. Perform a one-tailed test. Carry intermediate computations to 3 or more decimal places and round answers as specified.
To qualify for a medical study, an applicant must have systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, find the upper and lower limits of blood pressure a person must have to qualify for the study.
According to a report published by the USDA 3 years ago, a typical American consumes an average of 26 pounds of ice cream per year. A researcher at the USDA would like to determine if the average amount of ice cream consumed each year by a typical American has changed since the original report was published. The researcher collected data from a random sample of 65 Americans and found that the mean amount of ice cream consumed each year by the sample was 25.54 pounds with a standard deviation of 1.64 pounds. Using α=0.02, test the hypothesis that the mean amount of ice cream consumed each year by a typical American is different than 26 pounds. Use the p-value method. State the null and alternative hypothesis for this test. H0= H1= Determine the test statistic for the hypothesis test. Round the solution to four decimal places. =
The number of violent crimes committed in a day possesses a distribution with a mean of 2.1 crimes per day and a standard deviation of 5 crimes per day. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

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