CIE A Maths - Statistics Review

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons.  What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

• .0057
• .025
• .345
• .781

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

• .430
• .148
• .281
• .087

If X~Po(1.8), find P(2≤X≤4)

• 0.4285

• 0.7983

• 0.5008

• 0.7260

Salmi expected to receive 4 emails in a week. Find the probability of receiving 8 emails for the next 2 weeks.

• 0.0511

• 0.0297

• 0.5470

• 0.1395

If X~Po(λ) and P(X=0) = 0.0025, find λ.

• 5

• 0

• 4

• 6

The mean weight of a bag checked in at Southwest Airlines is 36 pounds with a standard deviation of 3.5 pounds. If two random bags were checked, what is the mean and the standard deviation of the weights of the two bags?

• 36, 4.95

• 36, 7

• 72, 4.95

• 72, 7

The mean weight of a dog is 34 pounds with a standard deviation of 6.7 pounds. The mean weight of a cat is 12 pounds with a standard deviation of 3.1 pounds. If you have 2 dogs and 1 cat, what is the mean and standard deviation of their total weight?

• 80, 9.969

• 80, 16.5

• 46, 7.382

• 46, 16.5

When you add a positive constant to a random variable the effects on the random variables distribution are as follows:

• the shape is changed, the mean is increased by a value of "a" and the standard deviation is unchanged.

• the shape and standard deviation are unchanged and the mean is increased by a value of "a".

• all three aspects are unchanged

• the shape and mean are unchanged and the standard deviation is increased by a value of "a".

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

• 0.90

• 1.155

• 1.645

• ±1.645

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)