Question

A) The total distances covered by GIMPA Undergraduate students to and from their work places every month is normally distributed with a mean 105 km and variance of 225 km2. a. What percentage of the population of students covered less than 90 km in a month in other words what is the probability of finding a student who covers less than 90 km in a month? (1 mark) b. The percentage of students who cover above 140 km every month (1 mark) c. The percentage of students who cover between 100 and 120 km every month (1 mark) d. What is the least distance of the top 0.1 decile category of the distances covered by students in a month? (2 mark) B) A health clinic found that in a sample of 200 women, the mean and the standard deviation of their masses are 85.5kg and 10.5kg, respectively. Also, 115 women were found to be over-weight. a. Find point estimates of the mean mass and proportion of over-weight in women population. (1 mark) b. Construct a 95% confidence interval for population mean mass. ( 2 marks) c. Construct a 95% confidence for proportion of over-weight in women population. (2marks)

Answer 1

Solution :

A):

a)0.1587

b) 1%

c) 47.06%

d) 124 km

B) :

a)Point estimate of mean mass is 85.5kg

Proportion of overweight womens is 0.575

b)95% confidence interval for mean mass is between 84.04kg & 86.95kg.

95% confidence interval for proportion of overweight women is between 0.51 &0.64.

Explanation :

Now , right tailed standard normal table is given below which is use for finding probabilities and z-score in above solution.