Exam 6: Normal Probability Distributions

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of $0 ^ { \circ } \mathrm { C }$ 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 $0 ^ { \circ } \mathrm { C }$ (denoted by negative numbers) and some give readings above $0 ^ { \circ } \mathrm { C }$ (denoted by positive numbers). Assume that the mean reading is $0 ^ { \circ } \mathrm { C }$ and the standard deviation of the readings is $1.00 ^ { \circ } \mathrm { C }$ Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. -If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the Rejected thermometers from the others.

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

Solve the problem. -A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 76.

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

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. -n = 16 and p = 0.2

What is the probability that the random variable has a value greater than 5?

Solve the problem. -The systolic blood pressure (in mmHg) is given below for a sample of 12 men aged between 60 and 65. 127 135 118 164 143 130 125 153 120 173 140 180

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5?

Solve the problem. -The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 Lb?

The population of current statistics students has ages with mean $\mu$ and standard deviation σ. 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?

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 15.2$ .2 and the standard deviation is $\sigma = 0.9$ Find the probability that X is greater than 17.

Solve the problem. -For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

Solve the problem. Round to the nearest tenth unless indicated otherwise. -The amount of rainfall in January in a certain city is normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. Find the value of the quartile Q1.

Solve the problem. -Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 Inches and 64.0 inches.

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?

Solve the problem. -A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70.

Solve the problem. -A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier 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 exceeds 8.7 hours.

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.

Solve the problem. Round to the nearest tenth unless indicated otherwise. -Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%. Round to the nearest hundredth of a Degree.

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.