 Hello and welcome to the session. In this session we will discuss a question which says that the amount of air in a sample of basket balls is normally distributed with mean 8 pounds at a standard variation of 0.5 pounds. What is the probability that a basket ball has less than 7 pounds or more than 9 pounds of air? Now before starting the solution of this question we should know some results. First is the graph of normal distribution is symmetric about the mean. Now this is the graph of normal distribution and you can see that it is symmetric about the mean here x bar denotes the mean and sigma denotes the standard variation. Here you can see about 68% of the data or area lies between x bar minus sigma and then about 95% of the data or area lies between x bar minus 2 sigma and x bar plus 2 sigma. About 99% of the data or area lies between x bar minus 3 sigma area on the curve gives the probability. Now these results will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now here we are given the average amount of air in a sample of basket balls that is 8 pounds and standard variation is 0.5 so we are given mean that is x bar is equal to 2 that is sigma is equal to 0.5. Now it is given to be a normal distribution. We first draw normal curve and to draw a normal curve we take horizontal axis. So here we have taken horizontal axis. Now to draw curve we have to find that is x bar minus sigma x bar minus 2 sigma x bar minus 3 sigma bar plus sigma 2 sigma x bar plus 3 sigma first of all let us find x bar minus sigma. Now it is equal to 8 minus 0.5 which is equal to 7.5. Then x bar plus sigma is equal to 8 plus 0.5 which is equal to 8.5 minus 2 sigma is equal to 8 minus 2 into 0.5 which is equal to 8 minus 1 that is equal to 7 plus 2 sigma is equal to 8 plus 2 into 0.5 which is equal to 8 plus 1 that is equal to 9 minus 3 sigma into 0.5 which is equal to 8 plus 1.5 that is equal to 6.5 plus 3 sigma is equal to 8 plus 3 into 0.5 that is equal to 8. Now we will draw vertical lines at these points. So we have drawn vertical lines at these points keeping in mind the symmetry about the mean that what is the probability. A basket ball has less than 9 pounds of air of data or percentage of area lying. Now from the key idea we know the percentage distribution of area for the graph of normal distribution so a graph of normal distribution which is symmetric about the mean the following percentage distribution of area. Now here we have to find the line above 9. The percentage of area lying between 9 plus 2 sigma is 5 percent plus 34 percent plus 34 percent 5 percent. 95 percent sigma is 9. This means percentage of area lying between 7 and 9 is 95 percent. Rest of the area lies below 7 covered between 100 percent between 7 and 9 is 95 percent is equal to 100 percent minus 95 percent lying above 9 and below 7 is equal to 5 percent. That percentage of area under the curve gives the probability under the curve that lies above 9 and below 7 basket ball has less than 7 pounds or more than 9 pounds of air at 05. This is the required answer. And this completes our session. Hope you all have enjoyed the session.