population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ . What is the probability that the sample mean will be within +/- 5 of the population mean?

A population has a mean of 200 and a standard deviation of 90. Suppose a simple random sample of size 125 is selected and is used to estimate μ. Use z-table. a. What is the probability that the sample mean will be within 18 of the population mean (to 4 decimals)? b. What is the probability that the sample mean will be within 16 of the population mean (to 4 decimals)?

An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is within 7 IQ points of the true mean. Assume that σ=14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100. A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15. Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance?   Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and why

A sample is selected from a normal population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean an extreme, unrepresentative value for the population

An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 4 IQ points of the true mean. Assume that σ=10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The random variable Z has mean 30 and variance 225. Calculate the limits between which you would expect the bulk of observations to lie for the random variable Z/3 − 7.

Assume all populations are normally distributed. A travel analyst claims that the mean price of a round trip flight from New York City to Los Angeles is less than $507. In a random sample of 55 round trip flights from NYC to LA, the mean price is $502. Assume the population standard deviation is $111. At α = 0.05, is there enough evidence to support the travel analyst’s claim?