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 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.
The weights of apples of a certain variety are normally distributed with mean 82 grams. 22\% of these apples have a weight greater than 87 grams.
Find the standard deviation of the weights of these apples.
Find the probability that the weight of a randomly chosen apple of this variety differs from the mean weight by less than 4 grams.
In a certain town, the time, X hours, for which people watch television in a week has a normal distribution with mean 15.8 hours and standard deviation 4.2 hours.
Find the probability that a randomly chosen person from this town watches television for less than 21 hours in a week.
Find the value of k such that P(X<k)=0.75.
Pia runs 2 km every day and her times in minutes are normally distributed with mean 10.1 and standard deviation 1.3.
Find the probability that on a randomly chosen day Pia takes longer than 11.3 minutes to run 2 km .
On 75 % of days, Pia takes longer than t minutes to run 2 km . Find the value of t.
On how many days in a period of 90 days would you expect Pia to take between 8.9 and 11.3 minutes to run 2 km ?
The weights, in kg , of bags of rice produced by Anders have the distribution N(2.02,0.032).
Find the probability that a randomly chosen bag of rice produced by Anders weighs between 1.98 and 2.03 kg .
The weights of bags of rice produced by Binders are normally distributed with mean 2.55 kg and standard deviation σkg. In a random sample of 5000 of these bags, 134 weighed more than 2.6 kg .
Find the value of σ.
A petrol station finds that its daily sales, in litres, are normally distributed with mean 4520 and standard deviation 560.
Find on how many days of the year (365 days) the daily sales can be expected to exceed 3900 litres.
The daily sales at another petrol station are X litres, where X is normally distributed with mean m and standard deviation 560. It is given that P(X>8000)=0.122.
Find the value of m.
Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution with mean 40 m and standard deviation 12 m . Trees with a height of less than 25 m are classified as short.
Find the probability that a randomly chosen tree is classified as short.
Of the trees that are classified as tall or medium, one third are tall and two thirds are medium.
Show that the probability that a randomly chosen tree is classified as tall is 0.298 , correct to 3 decimal places.
Find the height above which trees are classified as tall.
The weights of male leopards in a particular region are normally distributed with mean 55 kg and standard deviation 6 kg .
Find the probability that a randomly chosen male leopard from this region weighs between 46 and 62 kg.
The weights of female leopards in this region are normally distributed with mean 42 kg and standard deviation σ kg. It is known that 25% of female leopards in the region weigh less than 36 kg.
Find the value of σ.
The distributions of the weights of male and female leopards are independent of each other. A male leopard and a female leopard are each chosen at random.
Find the probability that both the weights of these leopards are less than 46 kg.