Applied Statistics
Tutorial Sheet 4.
1. The gestation period is approximately normally distributed with a mean of 275 days and a standard
deviation of 4.5 days. Estimate the probability that the gestation period is
i) greater than 280 days
ii) less than 265 days
iii) between 272 and 282 days.
iv) What gestation period is surpassed by 2.5% of the population?
2. The length of the jump of an athlete has a normal distribution with mean 7m and standard deviation
0.1m. Calculate the probability that he jumps
i) at least 7.15m
ii) between 6.9 and 7.05m
iii) Find the probability that if he jumps 3 times all the jumps will be less than 7.15m (assume the lengths
of the jumps are independent and use the answer to part i).
3. The monthly income of full time workers in the UK (in £) has a Pareto distribution with parameters
1000 and 3.
i) The expected (mean) salary.
ii) The probability that an individual earns above the mean salary.
iii) The probability that an individual earns below 2000.
iv) The probability that an individual earns between 3000 and 4000.
v) The median salary.
vi) The monthly salary which is exceeded by 10% of full-time workers.
vii) Out of 6 randomly chosen full-time workers, only one earns more than 2000 (see iii).
4. A sample of 300 households in a large town revealed that 183 have home computers. Construct 95%
and 99% confidence intervals for the proportion of households with home computers in the whole town.
5. What sample size is required to estimate a proportion to within 1% with a confidence level of 95%?
6. a) The average height of 100 Irish students was 1.72m and the variance 0.0144m2. Calculate 95%
and 99% confidence intervals for the average height of all Irish students.
b) Estimate the sample size required to estimate the mean height of all Irish students to within 1cm
with a confidence level of 95%.
7. The mean wage of 16 full-time workers in Ireland was €2500 and the standard deviation €1500.
a) Calculate a 95% confidence interval for the mean wage of all full-time workers in Ireland.
b) What assumption is made in this calculation? Is this assumption reasonable?