Question

Consider results of 20 randomly chosen people who have run a marathon. Their times, in minutes, are as follows: 140,145,154,162, 167,177,188,190,198,209,218,223,234,239,250,267,275,279,285,291. Calculate a 95% upper confidence bound on the mean time of the race. Assume distribution to be normal. Round your answer to the nearest integer (e.g. 9876).

Answer 1

To calculate the 95% upper confidence bound on the mean time of the race, use the formula: Upper bound = mean + (z * standard deviation / sqrt(n)). Using the given data, the upper bound is 231 minutes.

Step-by-step explanation:

To calculate the 95% upper confidence bound on the mean time of the race, you can use the formula:

Upper bound = mean + (z * standard deviation / sqrt(n))
where:
mean = average time of the race,
z = z-score corresponding to the desired confidence level (for 95% confidence level, z = 1.96),
standard deviation = standard deviation of the race times,
n = number of observations.

Using the given data, the mean time is 209.95 minutes, standard deviation is 51.77 minutes, and n is 20. Plugging these values into the formula, we get:

Upper bound = 209.95 + (1.96 * 51.77 / sqrt(20))
= 209.95 + (1.96 * 11.57)
= 231.31

Rounding the upper bound to the nearest integer, we get the 95% upper confidence bound on the mean time of the race as 231 minutes.