Exam 6: Normal Probability Distributions

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a __________equal to the _________ of The corresponding parameter.

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per Microliter. Approximately what percentage of women have red blood cell counts in the Normal range from 4.2 to 5.4 million cells per microliter?

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Two percent of hair dryers produced in a certain plant are Defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 Are defective.

Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 5, 7, and 9. Consider the values of 5, 7, and 9 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 5, 7, and 9. The nine different samples are as follows: (5, 5), (5, 7), (5, 9), (7, 5), (7, 7), (7, 9), (9, 5), (9, 7), and (9, 9). (i)Find the mean of each of the nine samples, then summarize the sampling distribution of the means in the format of a table representing the probability distribution. (ii)Compare the population mean to the mean of the sample means. (iii)Do the sample means target the value of the population mean? In general, do means make good estimators of population means? Why or why not?

Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a)Find the probability of a pregnancy lasting more than 250 days. (b)Find the probability of a pregnancy lasting more than 280 days. Draw the diagram for each and discuss the part of the solution that would be different for finding the requested probabilities.

The population of current statistics students has ages with mean $\mu$ and standard deviation $\sigma$ . Samples of statistics are randomly selected so that there are exactly 40 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages?

SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). (a)If a single student is randomly selected, find the probability that the sample mean is above 500. (b)If a sample of 35 students are selected randomly, find the probability that the sample mean is above 500. These two problems appear to be very similar. Which problem requires the application of the central limit theorem, and in what way does the solution process differ between the two problems?

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy last at least 300 days?

Assume that $z$ scores are normally distributed with a mean of 0 and a standard deviation of 1 . If $P ( - a < z < a ) = 0.4314$ , find $a$ .

In a population of 210 women, the heights of the women are normally distributed with a mean of $64.4$ inches and a standard deviation of $2.9$ inches. If 36 women are selected at random, find the mean $\mu _ { \bar { x } }$ and standard deviation $\sigma _ { \bar { x } }$ of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.

In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a Randomly selected home, find the probability that the September energy consumption level is Between 1100 kWh and 1225 kWh.

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform Distribution. Find the probability that the given range of pounds lost is between 8 pounds And 11 pounds.

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives. Use the normal distribution to approximate the desired probability.

The number of books sold over the course of the four-day book fair were 194, 197, 247, and 76. Assume that samples of size 2 are randomly selected with replacement from this population of four values. List the different possible samples, and find the mean of each of them.

A coin is tossed 20 times. A person who claims to have extrasensory perception is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the Probability of being correct 14 or more times by guessing? Does this probability seem to Verify her claim? Use the normal distribution to approximate the desired probability.

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these Thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers)and some give readings above 0°C (denoted by positive Numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1)00°C. Also assume that the frequency distribution of errors closely resembles the normal Distribution. A thermometer is randomly selected and tested. A quality control analyst wants To examine thermometers that give readings in the bottom 4%. Find the temperature reading That separates the bottom 4% from the others.