The average starting salary for a data analyst is Php 40,000 and a standard deviation of 5,000. A random sample of size 50 is drawn from the population. Find the probability that the sample mean X is less than 30,000.
The average starting salary for a data analyst is Php 40,000 and a standard deviation of 5,000. A random sample of size 50 is drawn from the population. Find the probability that the sample mean X is less than 30,000.
The average starting salary for a data analyst is Php 40,000 and a standard deviation of 5,000. A random sample of size 50 is drawn from the population. Find the probability that the sample mean X is less than 30,000.
6. The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis regardless of their other qualification?
Transcribed Image Text:The average starting salary for a data analyst is Php 40,000 and a standard deviation of 5,000. A random
sample of size 50 is drawn from the population. Find the probability that the sample mean X is less than
1.
30,000.
2.
A population has mean 555 and standard deviation 40.
Find the mean and standard deviation of sample means for samples of size 50.
Find the probability that the mean of a sample of size 50 will be more than 570.
A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles.
Five such tires are manufactured and tested. On the assumption that the actual population mean is
3.
38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the
sample mean will be less than 35,000 miles. Assume that the distribution of lifetimes of such tires is
normal.
4.
A normally distributed population has mean 1,200 and standard deviation 120.
Find the probability that a single randomly selected element X of the population is between 1,100 and
1,300.
Find the mean and standard deviation of X for samples of size 25.
Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100
and 1,300.
5.
Scores on an entrance exam in a large university, freshman course are normally distributed with mean 72.5
and standard deviation 13.0.
Find the probability that the score X on a randomly selected exam paper is between 70 and 80.
Find the probability that the mean score X of 40 randomly selected exam papers is between 70 and 80.
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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