STP231 HW 11

Weights of adult human brains are normally distributed. Samples of weights of adult human​ brains, each of size n=​15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too​ small? Explain.

It is not correct. The sample means can be treated as being from a normal distribution because the sample weights come from a population that is normally distributed.

A variable of a population has a mean of muequals73 and a standard deviation of sigmaequals6. a. Identify the sampling distribution of the sample mean for samples of size 36. b. In answering part​ (a), what assumptions did you make about the distribution of the​ var

normal 73 1 No assumptions were made​ because, for a relatively large sample​ size, the sampling distribution is​ normal, regardless of the distribution of the variable under consideration. No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

sampling distribution

of the mean is the probability distribution of sample means, with all samples having the same sample size n

uniform distribution

A continuous random variable has a uniform distribution if its values are spread evenly over the range of possibilities.

Normal distribution

If a continuous random variable has a distribution with a graph that is symmetric and​ bell-shaped, then it has a normal distribution.

probabilty distribution

Is a graph, table or formula that gives the probability for each value of a random variable

A researcher collects a simple random sample of​ grade-point averages of biostatistics students and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal​ distribution?

The sample must have more than 30 ​values, or there must be evidence that the population of​ grade-point averages from statistics students has a normal distribution.

_____________ is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population

The sampling distribution of a statistic​ (such as a sample mean or sample​ proportion) is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.​ (The sampling distribution of a statistic is typically represented as a probability distribution in the format of a​ table, probability​ histogram, or​ formula.)

standard normal distribution

The standard normal distribution is a normal probability distribution with mu=0 and sigma=1.

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 75 beats per minute. =.6255 b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. =.7389 c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

random variable

is a variable that has a single numerical value, determined by chance, for each outcome of a procedure