Quiz #5 1. True or False. Justify for full credit. (a) The normal distribution curve is...
Quiz #5 1. True or False. Justify for full credit. (a) The normal distribution curve is always symmetric to 0. (b) If the variance from a data set is zero, then all the observations in this data set are identical. (c) P(A OR A complement) =1, where A complement is the complement of A. (d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis. (e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
2.. What is the probability that a randomly selected person has an IQ between 85 and 115?
3. Find the 90th percentile of the IQ distribution.
4. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
5. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit.
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Quiz #5 1. True or False. Justify for full credit. (a) The
normal distribution curve is...
Problem 4. The lifetime of a certain battery follows a normal distribution with a mean of...
Problem 4. The lifetime of a certain battery follows a normal distribution with a mean of 276 and standard deviation of 20 minutes. (a) What proportion of the batteries have a lifetime more than 270 minutes? (b) Find the 90th percentile of the lifetime of these batteries. (c) We took a random sample of 100 batteries. What is the probability that the sample mean of lifetimes will be less than 270 minutes?
1. An electric firm manufactures light bulbs that have a lifetime, X, that is approximately norma...
1. An electric firm manufactures light bulbs that have a lifetime, X, that is approximately normally distributed with a standard deviation of 100 hours. Prior experience leads the firm to establish that the mean of X (or mean lifetime), say , follows a normal distribution with mean 140-800 hours and standard deviation σ0 10 hours. If a random sample of 25 bulbs examined turns out an average lifetime of 780 hours, solve the following. (a) Find a 95% Bayesian estinate...
Light bulbs with a stated mean lifetime of 750 hours have been stored in a warehouse...
Light bulbs with a stated mean lifetime of 750 hours have been stored in a warehouse for years . A sample of 10 of these bulbs is selected at random and destructively tested . The results of this sample gave a mean of 720 hours with a standard deviation of 40 hours . You wish to test whether prolong storage has significantly reduced the life expectancy of these light bulbs . You can assume that bulb lifetime is normally distributed....
Problem 1: The credit card debt for college seniors has a normal distribution with a mean...
Problem 1: The credit card debt for college seniors has a normal distribution with a mean of $3262 and a standard deviation of $1100. Consider credit card debt of a random sample of 16 college seniors. What is the distribution of mean credit card debt of 16 sampled college seniors? Provide name, mean and standard deviation of the distribution. Problem 2: The following figure shows the distribution of a population. 0.10 0.0 0.06 0.04 0.02 0.00 (a) What is the...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
answer a-f, clearly show the steps thanks 1. . The lifetimes of light bulbs produced by...
answer a-f, clearly show the steps thanks
1. . The lifetimes of light bulbs produced by a particular manufacturer have mean 1,200 hours and standard deviation 400 hours, The population distribution is normal. Suppose that you purchase 16 bulbs, which can be regarded as a random sample from the' manufacturer's output. a)What is the mean of the sample mean lifetime? Explain. bWhat is the standard error of the sample mean? Explain. c)What is the probability that, on average, these 16...
Fluorescent lighbulbs have lifetimes that follow a normal distribution, with an average life of 1,725 days...
Fluorescent lighbulbs have lifetimes that follow a normal distribution, with an average life of 1,725 days and a standard deviation of 1,462 hours. In the production process the manufacturer draws random samples of 215 lightbulbs and determines the mean lifetime of the sample. What would be the standard deviation, in hours, of the sampling distribution? Std. dev. of sample means (1 decimal place):
a. The drying time of a type of paint under specified test condition is known to...
a. The drying time of a type of paint under specified test condition is known to be normally distributed with an assumed mean value of 75 and a standard deviation of 9. Test the hypothesis H0: µ=75 vs. Ha: µ<75 from a sample of 25 observations. For a test procedure with α= 0.002 what is the probability of making a type 2 error when the true mean is 70, ß(70) (to 4 decimals)? b. Lightbulbs of a certain type are...
(1 point) The distribution of IQ scores can be modeled by a normal distribution with mean...
(1 point) The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15. (a) Let x be a person's IQ score. Write the formula for the density function of IQ scores. p(x) = (b) Estimate the fraction of the population with IQ between 80 and 85. fraction =
Problem 4. The lifetime of a certain battery follows a normal distribution with a mean of 276 and standard deviation of 20 minutes. (a) What proportion of the batteries have a lifetime more than 270 minutes? (b) Find the 90th percentile of the lifetime of these batteries. (c) We took a random sample of 100 batteries. What is the probability that the sample mean of lifetimes will be less than 270 minutes?
1. An electric firm manufactures light bulbs that have a lifetime, X, that is approximately normally distributed with a standard deviation of 100 hours. Prior experience leads the firm to establish that the mean of X (or mean lifetime), say , follows a normal distribution with mean 140-800 hours and standard deviation σ0 10 hours. If a random sample of 25 bulbs examined turns out an average lifetime of 780 hours, solve the following. (a) Find a 95% Bayesian estinate...
Problem 1: The credit card debt for college seniors has a normal distribution with a mean of $3262 and a standard deviation of $1100. Consider credit card debt of a random sample of 16 college seniors. What is the distribution of mean credit card debt of 16 sampled college seniors? Provide name, mean and standard deviation of the distribution. Problem 2: The following figure shows the distribution of a population. 0.10 0.0 0.06 0.04 0.02 0.00 (a) What is the...
answer a-f, clearly show the steps thanks
1. . The lifetimes of light bulbs produced by a particular manufacturer have mean 1,200 hours and standard deviation 400 hours, The population distribution is normal. Suppose that you purchase 16 bulbs, which can be regarded as a random sample from the' manufacturer's output. a)What is the mean of the sample mean lifetime? Explain. bWhat is the standard error of the sample mean? Explain. c)What is the probability that, on average, these 16...
(1 point) The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15. (a) Let x be a person's IQ score. Write the formula for the density function of IQ scores. p(x) = (b) Estimate the fraction of the population with IQ between 80 and 85. fraction =
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