In a Hyrox Fitness Challenge, the official finish times of 150 participants from Regent Polytechnic were recorded.
The table shows the time, \(t\) minutes, taken by the participants.
| Time, \(t\) minutes | \(50<t\le70\) | \(70<t\le90\) | \(90<t\le110\) | \(110<t\le130\) | \(130<t\le150\) |
|---|
| Frequency | \(12\) | \(29\) | \(x\) | \(39\) | \(21\) |
Find the value of \(x\).[1]
Calculate an estimate of the mean time taken.[1]
Calculate an estimate of standard deviation of the times taken.[1]
Another set of 150 participants from Summit Polytechnic have an estimated mean finish time of 99.5 minutes and standard deviation of 25.6 minutes.
A commentator says that participants from Summit Polytechnic performed better than those in Regent Polytechnic.
Explain why this comment is not fully justified.[2]
The histogram shows the distribution of time, \(t\) minutes, taken by 100 participants in a SkiErg challenge.
A participant who completes the SkiErg Challenge in at most 5 minutes is called a fast finisher.
Two participants are selected at random for an interview. Find the probability that both participants are fast finisher.[2]
Three participants are selected randomly for a photoshoot. Find the probability that at least one of them is a fast finisher.[2]
A coach claims that the number of participants who completed the SkiErg Challenge in less than 5.5 minutes is greater than the number who took more than 6.5 minutes.
Explain why his conclusion cannot be made from the histogram.[1]