Question

Lin Ying belongs to an athletic club. In 800 m races her times are normally distributed with mean 128 seconds and standard deviation

4 seconds.
(a) What is the probability of her time in an 800 being between 120 and 130 seconds?
(b) What time will she beat in 70% of her races?
Julie belongs to the same club. In 800 m races 85% of her times are less than 140 seconds and 70% are less than 135 seconds. Her times are normally distributed.
(c) Find the mean and standard deviation of Julie's times, each correct to two significant figures.
(d) What is the probability that in an 800 m race Lin Ying will beat Julie?
(e) The club has to choose one of these two athletes to enter a major competition. In order to qualify for the final rounds it is necessary to achieve a time of 114 seconds or less in the heats. Which athlete should be chosen and why?

Answer 1

Nine of the times for the first race were at least 16 seconds

Explanation:

Here we have from the scatter plot, the times are given as

Time Frequency

19 2

18 2

17 2

16 3

15 1

Therefore, total number of times that are above 16 seconds in the first race is

3 + 2 + 2 + 2 = 9

Therefore, the first option is correct

Answer 2

Explanation:

The answer is below. Plesetake a look and it will help you