Edexcel S1 2004 June — Question 5

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2004
SessionJune
TopicNormal Distribution
TypeFind standard deviation from probability

5. A health club lets members use, on each visit, its facilities for as long as they wish. The club's records suggest that the length of a visit can be modelled by a normal distribution with mean 90 minutes. Only \(20 \%\) of members stay for more than 125 minutes.
  1. Find the standard deviation of the normal distribution.
  2. Find the probability that a visit lasts less than 25 minutes. The club introduce a closing time of 10:00 pm. Tara arrives at the club at 8:00 pm.
  3. Explain whether or not this normal distribution is still a suitable model for the length of her visit.