Scores on a common final exam in a large enrollment, multiple-section freshman course are normally distributed with mean 72.7 and standard error of 1.31 for a sample of 100. (a) Find the probability that the score, X on a randomly selected exam paper is between 70 and 80. (b) (c) Find the probability that the mean score, X of 38 randomly selected exam papers is between 70 and 80. Calculate the minimum score that need to be scored by a student for the probability to exceed 95% of marks. QUESTION 9 (10 Marks) You are planning an outing in the afternoon to either visit Sungei Buloh Nature Reserve or watch a movie. Based on historical records, it rains 20% of the time and 50% of the time the sky is cloudy. 40% of all rainy days start off cloudy. (a) What is the chance of rain during the day when the sky is cloudy? (b) Briefly describe your finding and where you should go for the outing. QUESTION 10 (10 Marks) A dietetics student wants to look at the relationship between calcium intake and knowledge about calcium in sports science students. Furthermore, she wants to know if knowledge about calcium can be used to predict calcium intake of the students. Table 10 shows the data she collected. score (Out of 50) 10 42 38 15 22 (a) (b) Y-Calcium intake (mg/day) 450 1050 900 525 710 Table 10 Find the equation of the regression line and interpret the regression coefficients. What are the functions in excel to calculate Y-intercept and gradient of a simple linear regression?