EduNinjaThe times taken to swim 100 metres by members of a large swimming club have a normal distribution with mean 62 seconds and standard deviation 5 seconds.
Find the probability that a randomly chosen member of the club takes between 56 and 66 seconds to swim 100 metres.
13 % of the members of the club take more than t minutes to swim 100 metres. Find the value of t.
A company produces a particular type of metal rod. The lengths of these rods are normally distributed with mean 25.2 cm and standard deviation 0.4 cm . A random sample of 500 of these rods is chosen.
How many rods in this sample would you expect to have a length that is within 0.5 cm of the mean length?
The residents of Persham were surveyed about the reliability of their internet service. 12\% rated the service as 'poor', 36 % rated it as 'satisfactory' and 52 % rated it as 'good'.
A random sample of 8 residents of Persham is chosen.
A random sample of 125 residents of Persham is now chosen.
Use an approximation to find the probability that more than 72 of these residents rate their internet service as good.
In a large college, 32 % of the students have blue eyes. A random sample of 80 students is chosen. Use an approximation to find the probability that fewer than 20 of these students have blue eyes.
The lengths of the rods produced by a company are normally distributed with mean 55.6 mm and standard deviation 1.2 mm .
In a random sample of 400 of these rods, how many would you expect to have length less than 54.8 mm ?
Find the probability that a randomly chosen rod produced by this company has a length that is within half a standard deviation of the mean.
The weights of large bags of pasta produced by a company are normally distributed with mean 1.5 kg and standard deviation 0.05 kg .
Find the probability that a randomly chosen large bag of pasta weighs between 1.42 kg and 1.52 kg .
The weights of small bags of pasta produced by the company are normally distributed with mean 0.75 kg and standard deviation σkg. It is found that 68 % of these small bags have weight less than 0.9 kg .
Find the value of σ.
The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm .
Find the probability that a randomly chosen adult raccoon of this species has a tail length between 23 cm and 35 cm .
The masses of adult raccoons of this species are normally distributed with mean 8.5 kg and standard deviation σkg.75% of adult raccoons of this species have mass greater than 7.6 kg .
Find the value of σ.
The weights of bags of sugar are normally distributed with mean 1.04 kg and standard deviation σkg. In a random sample of 2000 bags of sugar, 72 weighed more than 1.10 kg .
Find the value of σ.
In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m .
Find the probability that an adult chosen at random from this country will have height greater than 1.93 m.
In another country, the heights of the adult population are also normally distributed. 33% of the adult population have height less than 1.56 m. 25% of the adult population have height greater than 1.86 m.
Find the mean and the standard deviation of this distribution.
Anil is a candidate in an election. He received 40\% of the votes. A random sample of 120 voters is chosen.
Use an approximation to find the probability that, of the 120 voters, between 36 and 54 inclusive voted for Anil.