Python code for the following statistical questions:

Problem 1 A physiotherapist with a male football team is interested in studying the relationship between foot injuries and the positions at which the players play from the data collected. : Attacking " Strike Forward Midfielder Winger Total Players 45 56 24 20 145 Injured Players Not 32 38 11 9 90 Injured Total 77 94 35 29 235 Based on the above data, answer the following questions. 1.1 What is the probability that a randomly chosen player would suffer an injury? 1.2 What is the probability that a player is a forward or a winger? 1.3 What is the probability that a randomly chosen player plays in a striker position and has & foot injury? 1.4 What is the probability that a randomly chosen injured player is a striker? Problem 2 The breaking strength of gunny bags used for packaging cement is normally distributed with a mean of 5 kg per sq. centimeter and a standard deviation of 1.5 kg per sq. centimeter. The guality team of the cement company wants to know the following about the packaging material to better understand wastage or pilferage within the supply chain; Answer the questions below based on the given information; (Provide an appropriate visual representation of your answers, without which marks will be deducted) 2.1 What proportion of the gunny bags have a breaking strength of less than 3.17 kg per sq cm'? 2.2 What proportion of the gunny bags have a breaking strength of at least 3.6 kg per sqcm.? 2.3 What proportion of the gunny bags have a breaking strength between 5 and 5.5 kg per sq cm.? 2.4 What proportion of the gunny bags have a breaking strength NOT between 3 and 7.5 kg persgcm.? Problem 3 Zingaro stone printing is a company that specializes in printing images or patterns on polished or unpolished stones. However, for the optimum level of printing of the image, the stone surface must have a Brinell's hardness index of at least 150. Recently, Zingaro has received a batch of polished and unpolished stones from its clients. Use the data provided to answer the following (assuming a 5% significance level); 3.1 Zingaro has reason to believe that the unpolished stones may not be suitable for printing. Do you think Zingaro is justified in thinking so? 3.2 Is the mean hardness of the polished and unpolished stones the same? Problem 4 Dental implant data: The hardness of metal implants in dental cavities depends on multiple factors, such as the method of implant, the temperature at which the metal is treated, the alloy used as well as the dentists who may favor one method above another and may work better in his/her favorite method. The response is the varniable of interest. 4.1 How does the hardness of implants vary depending on dentists? 4.2 How does the hardness of implants vary depending on methods? 4.3 What is the interaction effect between the dentist and method on the hardness of dental implants for each type of alloy? 4.4 How does the hardness of implants vary depending on dentists and methods together? \fDentist Method Alloy Temp Response 1 1500 813 1600 792 1700 792 1500 907 1600 792 1700 835 1500 782 1600 698 1700 665 1500 1115 1600 835 1700 870 1500 752 1600 620 1700 835 1500 847 1600 560 1700 585 1500 715 1600 803 1700 813 1500 858 1600 907 1700 882 1500 772 1600 782 1700 743 1500 933 1600 792 1700 824 ( ( ( ( ( ( ( ( ( O O N N N N N N N N N N N N N N N N N N - 3 3 1500 835 1600 715 1700 673 1500 698 1600 734 1700 681 1500 743 1600 627 1700 752 1500 858 1600 762 1700 724 1500 813 1600 743 1700 613 1500 824 1600 847