Maths Studies - Normal Distribution

Malthouse school opens at 08:00 every morning.

The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.

Find the probability that a student, chosen at random arrives at least 60 minutes after the school opens.

• 0.0548

• 0.0547

• 0.567

• 0.9452

Malthouse school opens at 08:00 every morning.

The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.

Find the probability that a student, chosen at random arrives between 45 minutes and 55 minutes after the school opens.

• 0.644

• 0.645

• 0.355

• 0.3

Malthouse school opens at 08:00 every morning.

The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.

A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the students at this school follows exactly the same distribution as Malthouse school.

Given that, on one morning, 15 students arrive at least 60 minutes after the school opens, estimate the number of students at Mulberry Park school.

• 270

• 280

• 275

• 274

Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.

Find the probability that this applicant took at least 40 minutes to complete the test.

• 0.213

• 0.2211

• 0.787

• 0.888

Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.

For 11% of the applicants it took longer than minutes to complete the test.

Find the value of .

• 73

• 74

• 75

• 76

Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.

There were 400 applicants for the job.

Estimate the number of applicants who completed the test in less than 25 minutes.

• 14

• 16

• 20

• 25

The mass of a certain type of Chilean corncob follows a normal distribution with a mean of 400 grams and a standard deviation of 50 grams.

Write down the probability that the mass of one of these corncobs is greater than 400 grams.

• 0.5

• 0.25

• 0.98

• 0.997

The mass of a certain type of Chilean corncob follows a normal distribution with a mean of 400 grams and a standard deviation of 50 grams.

A farmer labels one of these corncobs as premium if its mass is greater than grams. 25% of these corncobs are labelled as premium.

Find the value of .

• 420

• 424

• 434

• 440

The weight, , of bags of rice follows a normal distribution with mean 1000 g and standard deviation 4 g.

Find the probability that a bag of rice chosen at random weighs between 990 g and 1004 g.

• 0.165

• 0.111

• 0.825

• 0.835

The weight, , of bags of rice follows a normal distribution with mean 1000 g and standard deviation 4 g.

95% of the bags of rice weigh less than grams.

Find the value of .

• 990

• 1000

• 1010

• 1020