5. IQ's are normally distributed with mean and standard deviation 15. Find the probability that a randomly selected person has an IQ between 100 and 115.
5. IQ's are normally distributed with mean and standard deviation 15. Find the probability that a randomly selected person has an IQ between 100 and 115.
5. IQ's are normally distributed with mean and standard deviation 15. Find the probability that a randomly selected person has an IQ between 100 and 115.
Transcribed Image Text:1. A softdrink machine is regulated so that it discharges an average of 200 milliliters per cup. If the
amount of drink is normally distributed with a standard deviation of 15 milliliters, what fraction of the
cups will contain more than 224 milliliters?
2. What is the probability that a cup contains between 191 and 209 milliliters?
3. How many cups will probably overflow if 230 milliliter cups are used for the next 1000 drinks?
4. Below what value do we get the smallest 25% of the drinks?
5. IQ's are normally distributed with mean and standard deviation 15. Find the probability that a
randomly selected person has an IQ between 100 and 115.
6. The loaves of rye bread distributed to local stores by a certain bakery have an average length of 30
centimeters and a standard deviation of 2 centimeters. Assuming that the lengths are normally distributed,
what percentage of the loaves are
(a) Longer than 31.7 centimeters?
(b) Between 29.3 and 33.5 centimeters in length?
(c) Shorter than 25.5 centimeters?
7. The weights of a large number of miniature poodles are approximately normally distributed with a
mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the
nearest tenth of a kilogram, find the fraction of these poodles with weights
(a) Over 9.5 kilograms;
(b) Of at most 8.6 kilograms;
(c) Between 7.3 and 9.1 kilograms.
8. A pair of dice is rolled 180 times. What is the probability that a total of 7 occurs
(a) At least 25 times?
(b) Between 33 and 41 times inclusive?
(c) Exactly 30 times?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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