Statistics Assignment
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1) Assume the random variable x is normally distributed with mean μ=8383 and standard deviation
σ=55. Find the indicated probability. P(68<x<76) =
2)In a survey of a group of men, the heights in the 2029 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.
(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is
(Round to four decimal places as needed.)
 b) Find the probability that a study participant has a height that is between 68 and 70 i
The probability that a study participant selected a random is vetween68 and 70 inches tall is ? ( round to four decimal places)
 c) Find the probability that a study participant has a height that is more than 70
The probability that the study participant selected at random is more than
70 inches tall is (Round to four decimal places as needed.)
d ) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
 there are no unusual events because all the probabilities are greater than 0.05.
 the event in part ( a) is unusual because its probability is less than 0.05
 The event in parts (a) (b) an (c) are unusual because all of their probabilities are less than 0.05.
 The events in parts (a) and (c) are unusual because its probabilities are less than 0.05.
3) to complete this question see attachment 5 please.
Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.
The probability that the member selected at random is from the shaded area of the graph is ? Round to four decimal places as needed.
4) Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 107. 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 525?
a) Approximately ? % of the SAT verbal scores are less than 650 ( round to ne nearest two decimal places as needed). b) You would expect that approximately ? SAT verbal scores would be greater than 525. (round to the nearest whole number as needed).
5) See attachment 1 and 2 to finish this question. in a survey of women in a certain country (ages 20minus−29), the mean height was 62.7 inches with a standard deviation of 2.93. inches. Answer the following questions about the specified normal distribution. a) What height represents the 95th percentile? b) What height represents the first quartile?
The height that represents the 95th percentile is ? inches. (Round to two decimal places as needed.) The height that represents the first quartile is ? inches. (Round to two decimal places as needed.)
6) See attachment 3 to finish this question The time spent (in days) waiting for a heart transplant for people ages 3549 can be approximiated by the normal distribution, as shown in the figure to the right. a) What waiting time represents the 55th percentile is ? days. (round to the nearest integer if needed) B) The waiting time that represents the third quartile is ? days.( (round to the nearest integer if needed)
7) A population has a mean μ=74 and a standard deviation σ =28. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=246. a) Find μ x = ? ( simplify your answer? b) Find σ x = ? (Type an integer or decimal rounded to three decimal places as needed) 8) Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $61,000. A random sample of 32 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58, 500?Assume σ=$5,500. The probability that the mean salary of the sample is less than $58 comma 50058,500 is ? .(Round to four decimal places as needed.)
9) A manufacturer claims that the life span of its tires is 47,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 46, 893 miles. Assume σ=800 Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 46,893 miles or less? ? (Round to four decimal places as needed.)
10) Construct the confidence interval for the population mean μ. c=0.98 , x=5.2, σ=0.4, and n =60 A 98% confidence interval for μ is (? , ? ) (Round to two decimal places as needed.)
11) You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? Ifconvenient, use technology to construct the confidence intervals. A random sample of 37 gas grills has a mean price of $640.70. Assume the population standard deviation is $56.30 – The 90% confidence interval is ( ? ; ?) Round to one decimal place as needed. – The 95% confidence interval is ( ?; ?)Round to one decimal place as needed. – Which interval is wider? Choose the correct answer below.
a) The 95% confidence interval
b) The 90% confidence interval
12) People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 99% confidence? Initial survey results indicate that σ=13.4 books. A 99% confidence level require ? subjects. Round up to the nearest whole number as needed.)
13) In a survey of 646 males ages 1864, 395 say they have gone to the dentist in the past year. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
– The 90% confidence interval for the population proportion p is ( ? ;? ) Round to three decimal places as needed. – The 95% confidence interval for the population proportion p is ( ?; ?) Round to three decimal places as needed. 14) A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their country’s banking system. His estimate must be accurate within 2% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they are confident with their country’s banking system.
What is the minimum sample size needed assuming that no prior information is available? n = ? Round up to the nearest whole number as needed. What is the minimum sample size needed using a prior study that found that 22% of the respondents said they are confident with their country’s banking system? n = ? Round up to the nearest whole number as needed. 15) To complete this question please see attachment 4 The table to the right shows the results of a survey in which 400 adults from the East, 400 adults from the South, 400 adults from theMidwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts (a) and (b). a) Construct a 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem. The 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is ( ?; ?) (Round to three decimal places as needed b) Construct a 99% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem. Is it possible that these two proportions are equal? Explain your reasoning. The 99% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem is ( ?;?) Round to three decimal places as needed. ORDER NOW your custom paper to have it completed successfully on time. Statistics Assignment
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