This table gives a probability that a statistic is less than Z (i.e. The table values are critical values of the t distribution. Note that for z = 1, 2, 3, one obtains (after multiplying by 2 to account for the interval) the results f( z) = 0.6827, 0.9545, 0.9974, Click here to view page 1 of the normal distribution table. The area either to the left of 0.64 or to the right of 1.69. The area either to the left of -1.75 or to the right of 1.34. Sketch a standard normal curve and shade the area of interest. 125 Пѓ = 29 + ( 1.If X is a random variable from a normal distribution with mean Ој and standard deviation Пѓ, its Z-score may be calculated from X by subtracting Ој and dividing by the standard deviation: Use a standard normal table to obtain the areas under the normal curve described below. The fastest and slowest times that are still considered average are x fast = Ој + ( в€’ z. 125, which by Figure 12.2 'Cumulative Normal Probability' is в€’1.15, and the slowest time that is вЂњaverageвЂќ has z-score z. Thus the fastest time that is вЂњaverageвЂќ has z-score в€’ z.

By the symmetry of the density curve each tail must have half of this total, or area 0.125 each. Because the area in the middle corresponding to вЂњaverageвЂќ times is 0.75, the areas of the two tails add up to 1 в€’ 0.75 = 0.25 in all. Thus the situation is as shown in Figure 5.27 'Distribution of Times to Run a Course'. The probability that X lie in a particular interval is the same as the proportion of all finish times that lie in that interval. Then X is normally distributed with mean 29 and standard deviation 2. Let X denote the finish time of a randomly selected boy. 2 thoughts on 3.1 Finding Areas Using the Standard Normal Table (for tables that give the area to left. The middle 75% of all finishing times are classified as вЂњaverage.вЂќ Find the range of times that are average finishing times by this definition. The table used is one that gives areas to the. Finishing times are normally distributed with mean 29 minutes and standard deviation 2 minutes. ДЄll boys at a military school must run a fixed course as fast as they can as part of a physical examination. Since 0.9901 is closer to 0.9900 than 0.9898 is, we use the column heading above it, 0.03, to obtain the approximation z. It is not there, but falls between the numbers 0.9898 and 0.9901 in the row with heading 2.3. Then we search for the area 0.9900 in Figure 12.2 'Cumulative Normal Probability'. See Figure 5.23 'Computation of the Number '. To begin with, we must first subtract 0.01 from 1 to find the area 1 в€’ 0.0100 = 0.9900 of the left tail cut off by the unknown number z. 01 first, and it is instructive to rework the problem this way. We could just as well have solved this problem by looking for z. 01 = в€’ 2.33, we conclude immediately that z. The answer to the second half of the problem is automatic: since в€’ z. 01 we use the heading of the column that contains 0.0099, namely, 0.03, and write в€’ z. Standard normal distribution table is used to find the area under the f(z) function in order to find the probability of a specified range of distribution. The normal distribution density function f(z) is called the Bell Curve because it has the shape that resembles a bell. The number 0.0099 is closer to 0.0100 than 0.0102 is, so for the hundredths place in в€’ z. Normal distribution is a continuous probability distribution. It is not there, but falls between the two numbers 0.0102 and 0.0099 in the row with heading в€’2.3. 01 cuts off a left tail of area 0.01 and Figure 12.2 'Cumulative Normal Probability' is a table of left tails, we look for the number 0.0100 in the interior of the table. Note that the probabilities given in this table represent the area to the LEFT of the z-score. The standard normal distribution follows the 68-95-99.70 Rule, which is also called as the Empirical Rule Empirical Rule Empirical Rule in Statistics states that almost all (95) of the observations in a normal distribution lie within 3 Standard Deviations from the Mean. 01, the values of Z that cut off right and left tails of area 0.01 in the standard normal distribution. Table of Standard Normal Probabilities for Positive Z-scores.

Standard normal table to the left