Distribution Math

A policeman inspected the safety of tyres on cars passing through a checkpoint. 

The number of tyres X which needed replacing on each car followed the probability distribution shown.

Find the value of k.

• 0.04

• 0.4

• 0

Find the expected value (mean) of the distribution.

• 1

• 2.45

• 0.6125

• unable to determine

The mass, W, of bags of rice follows a normal distribution with mean 1000 g & standard deviation 4 g.

     92% of the bags of rice have a mass more than k grams.

Find the value of k  .

• 994

• 1005

• 1

• 0

The car company chooses a sample of 50 ball bearings from the shipment. If they find more than 2 defective bearings, the shipment is rejected. It is a fact that the factory produces 4% defective bearings.

What is the probability that the sample is clear of defects?

• 0.271

• 0.130

• 0.002

P(X > 1) = 0.6 could mean . . .

• The probability that there is less than 1 head is 60%

• The probability that there is more than 1 head is 60%

• The probability that there is more than 60 heads is 1

Which is the correct notation for the following: The mass, W, of bags of rice follows a normal distribution with mean 1000 g & standard deviation 4 g.

A machine fills plastic bottles with mineral water. The volume of mineral water that the machine pours into each bottle follows a normal distribution with the mean of 498ml and a standard deviation of 3.4ml. Each bottle has a maximum capacity of 506ml. On the label of each bottle is printed the statement: Contents 500ml. Find the probability that a bottle chosen by random has a volume less than 500 ml

• 0.278

• -0.278

• 0.722

• 0.498

Find the standard deviation of a binomial distribution with n=50 and p=0.4 (Round to the nearest tenth)

• 4.2

• 3.5

• 12.0

• 6.2

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%

• 47.5%

• 68%

• 95%

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1

• No, not all P(x) values are between 0 and 1.

• No, ∑P(x) ≠ 1.