mean of a random sample of 100 students will be taller than 1.60 m? 4. A sample of the various prices for a particular product has been conducted in 16 stores that were selected at random in a neighborhood of a city. The following prices were noted: 95, 108, 97, 112, 99, 106, 105, 100, 99, 98, 104, 110, 107, 111, 103, 110. Assuming that the prices of this product follow a normal law of variance of 25 and an unknown mean: a . What is the distribution of the sample mean? b. Determine the confidence interval at 95% for the population mean. 5.The average height of a random sample of 400 people from a city is 1.75 In. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16. a. Determine the interval of 95% confidence for the average heights of the population. b. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm from the sample mean? 6. The monthly sales of an appliance shop are distributed according to a normal law, with a standard deviation of $900. A statistical study of sales in the last nine months has found a confidence interval for the mean of monthly sales with extremes of $4,663 and $5,839. a. What were the average sales over the nine-month period? b. What is the confidence level for this interval? 7. The proportion of colorblind individuals in a population needs to be estimated by the percentage observed in a random sample of individuals of size n. a. If the percentage of colorblind individuals in the sample is 30%, estimate the value of n so that, with a confidence level of 0.95, the error in the estimate is less than 3.1%. b. If the sample size is 64 individuals, and the percentage of colorblind individuals in the sample is 35%, determine using a significance level of 1%, the corresponding confidence interval for the proportion of the colorblind population. 8. In a population, a random variable follows a normal distribution with an unknown mean and a standard deviation of 2. a. In a sample of 400 selected at random, a sample mean of 50 was obtained. Determine the confidence interval with a confidence level of 97% for the average population. b. With the same confidence level, what minimum sample size should it have so that the interval Width has a maximum length of 1? 9. The quantity of hemoglobin in the blood spread of a man follows a normal distribution with a standard deviation of 2 g/dl
