Exam 6: Normal Probability Distributions

A normal quartile plot is given below for the lifetimes (in hours)of a sample of batteries of a particular brand. Use the plot to assess the normality of the lifetimes of these batteries. Explain your reasoning.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

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

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?

Which of the following is a biased estimator?

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less Than 8.9 hours.

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 }$ the score which separates the lower 60% from the top 40% .

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.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

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.

Estimate the probability of getting exactly 43 boys in 90 births. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

Identify three important criteria to determine if the use of a normal distribution is justified

For the binomial distribution with n=24 and p=0.6 , state whether or not it is suitable to use the normal distribution as an approximation.

The continuity correction is used to compensate for the fact that a ___________distribution is used to approximate a ____________ distribution.

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.

You will use a normal distribution to approximate a binomial distribution. Complete the following table for a distribution in which $\mu = 16$ It might be helpful to make a diagram to help you determine the continuity factor for each entry. Find the probability that The continuity correction factor is: x is at least 12 x is at most 12 x is more than 12 x is less than 12

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?

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.

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?