HOMEWORK
1. The height of students studying at a language school follows a normal distribution with a mean of 1.62 m and a standard deviation of 0.12. What is the probability that the mean of a random sample of 100 students will be taller than 1.60 m?
2. A sample of the various prices for a particular product has been conducted in 16 stores which 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.
What is the sample mean?
Determine the confidence interval at 95% for the population mean.
3. The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16.
Determine the interval of 95% confidence for the average heights of the population.
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?
4. The monthly sales of an appliance shop are distributed according to a normal distribution, 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.
What were the average sales over the nine month period?
What is the confidence level for this interval?
5. The proportion of color blind individuals in a population needs to be estimated by the percentage observed in a random sample of individuals of size n.
If the percentage of color blind 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%.
If the sample size is 64 individuals, and the percentage of color blind individuals in the sample is 35%, determine using a significance level of 1%, the corresponding confidence interval for the proportion of the color blind population.
6. In a population, a random variable follows a normal distribution with an unknown mean and a standard deviation of 2.
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.
With the same confidence level, what minimum sample size should it have so that the interval width has a maximum length of 1?
7. The quantity of hemoglobin in the blood spream of a man follows a normal distribution with a standard deviation of 2 g/dl. Calculate the confidence level for a sample of 12 men which indicates that the population mean blood hemoglobin is between 13 and 15g/dl.