Page < > of 5 5. Distribution of heights of Elderly English women is known to be normal with a mean of 156 cm and a standard deviation of 6 cm.We randomly choose a sample of 100 elderly English women. (a) Find mean ug and standard deviation ag of the distribution of sample means. (b) Is the shape of the distribution normal? In other words are the sample size conditions met? (c) Find probability that in a random sample of 100 elderly English women, the sample mean of heights is less than 155 cm. 0.0478 6. According to the Regional Bar Association, approximately 67% of the people who take the bar exam to practice law in the region pass the exam. Find the approximate probability that at least 68% randomly sampled 500 people taking the bar exam will pass. To answer the question, go through the following steps. (a) What is the symbol for 67%? (b) Find mean µg and standard deviation os of the distribution of sample proportions. (c) Are the sample size conditions for distribution to be normal met? (d) Find probability that sample proportion is more than 68%. 0.3172 7. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog. Suppose a random sample of 12 households with only one pet is selected. Use Binomial distribution to find the probability that 3 households will have a dog? Show work. 0.1526 8. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog. Suppose a random sample of 120 households with only one pet is selected. Desktop 72°F Sunny DELL