Statistics and Probability Answers

The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standard deviation of 0.3 hours. Calculate the following :
a. A random movie is between 1.8 and 2.0 hours
b. A movie is longer than 2.3 hours
c. The length of movie that is shorter than 94% of the movies

Marco counted 40 cars in the parking lot. 28 were silver. What is the experimental probability that the next car in the lot will be silver?

What is the probability that a random teacher is between 35 years and 55 years old, P(2<x>6)?

What is the probability that a random teacher from a high school is older than 45 years old, p(x>4)?

Two teachers have classes of similar sizes . After the final exams, the mean of the grades in each class is 73%. However, one class has a standard deviation of 4% while the other is 8%. In which class would a mark of 90% be more meaningful?

An agency is conducting performance tests on different brands of skateboard. Tests show that the pressure, in pounds per square inch, required to break the boards is normally distributed with a mean of 54.7 and a standard deviation of 6.2

a. What percent of the boards have breaking pressures between 50 and 60?
b. What is the probability that any board will require at least a pressure of 70 to break ?
c. In what range centred on the mean will 80% of the data lie?

Historically the results of a final exam given by a particular teacher have a mean of 65.3% with a standard deviation of 8.5

a. Calculate the probability of a student getting a mark between i. 75 and 85 ii. 79 and 81 iii. 79.9 and 80.1
b. Based on these results , a student says, “it’s almost impossible to get an 80 on the exam.” Comment on whether this is true

The weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg , with a standard deviation of 0.4 kg

a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg ?
b. A car is said to be in the 90th percentile. How much does it weigh?

IQ scores of people around the World are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius ?

For a mean of 153 and a standard deviation of 25, find P(130 ≤ x ≤ 170 )