**Emma’s On-the-Go** is a large convenience store experimenting with different locations for its candy bar display to increase sales. The three locations considered are:1. **Front of the store**: To attract “impulse buying” from all customers.2. **Left-hand side of the store**: To attract teenagers.3. **Back of the store**: To attract adults.The manager rotates the candy display across these areas, collecting data over 48 days for each. The table below shows the sample mean daily sales (in dollars) and the sample variances for each location.| Group | Sample size | Sample mean | Sample variance ||------------------|-------------|-------------|-----------------|| Front of store | 48 | 209.4 | 465.4 || Left-hand side | 48 | 222.4 | 553.5 || Back of store | 48 | 204.8 | 482.0 |The populations of daily sales from which these samples are drawn are assumed to be approximately normally distributed, each with the same mean and variance.**Tasks:**1. **(a)** Estimate the common population variance by pooling the sample variances given.2. **(b)** Estimate the common population variance based on the variance of the sample means.Calculations should maintain at least three decimal places, and responses should be rounded to one decimal place. Emma's On-the-Go, a large convenience store that makes a good deal of money from candy bar sales, has three possible locations in the store for its candy bar display: in the front of the store (to attract "impulse buying" by all customers who enter), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of many months by rotating the candy bar display among the three locations, choosing a sample of 48 days at each location. Each day, the manager records the amount of money brought in from the sale of candy bars.Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances:| Group | Sample size | Sample mean | Sample variance ||-----------------|-------------|-------------|-----------------|| Front of store | 48 | 209.4 | 465.4 || Left-hand side | 48 | 222.4 | 453.5 || Back of store | 48 | 204.8 | 482.0 |Buttons: - Send data to calculator- Send data to ExcelAssume that the populations of daily sales from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance.Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.(a) Give an estimate of this common population variance by pooling the sample variances given.(b) Give an estimate of this common population variance based on the variance of the sample means given.

a) Estimate of the common variance by pooling the sample variances: Variance=n1-1s12+n2-1s22+n2-1s22n1+n2+n3-3 =48-1465.4+48-1553.5+48-148248+48+48-3 =70542.3141 =500.3b) Estimate of the common population variance based on the variance of the sample means: Consider, the mean of the sample means, x¯¯=∑x¯n =209.4+222.4+204.83 =212.2 Consider, the estimate, s2=∑x¯-x¯¯2n-1 =209.4-212.22+222.4-212.22+204.8-212.223-1 =83.32