Exam 6: The Normal Probability Distribution

Given that z is a standard normal variable, which of the following is the value for which P(z ) = 0.242?

The relative frequency associated with a particular class in the population is the probability of drawing a measurement from that class.

In general, the binomial probability P(X x) is approximated by the area under the normal curve to the right of x - 0.5.

Blood Types Narrative In a certain population, 18% of the people have Rh-negative blood. A blood bank serving this population receives 95 blood donors on a particular day. -Refer to Blood Types Narrative. What is the probability that 15 to 20 (inclusive) of the donors are Rh-negative?

Tar Amounts in Cigarettes Narrative Suppose the amount of tar in cigarettes is normally distributed, with mean 3.5 mg and standard deviation 0.5 mg. -Refer to Tar Amounts in Cigarettes Narrative. What proportion of cigarettes have a tar content exceeding 4.25 mg?

Which of the following is always true for all probability density functions of continuous random variables?

Pacific Salmon Narrative The owner of a fish market determined that the average weight for a Pacific salmon is 3.6 kg, with a standard deviation of 0.8 kg. Assume the weights of the salmon are normally distributed. -Refer to Pacific Salmon Narrative. Above what weight do 87.70% of the weights occur?

Even though the normal probability distribution deals with continuous variables, we can use it to approximate the binomial probability distribution whenever n 30 and also n(q) 30.

The time necessary to assemble a discount store display is normally distributed, with = 5 minutes and = 30 seconds. A large number of potential employees are timed assembling a practice display. How much time (in minutes) should the personnel manager allow the potential employees to assemble the display if the store wants only 80% of the people to complete the task?

High School Graduates IQ's The distribution of IQ scores for high school graduates is normally distributed with = 104 and = 16. -Refer to High School Graduates IQ's paragraph. What percentage of the IQ scores would be between 97 and 126?

Which of the following values is the z-score representing the first quartile of the standard normal distribution?

Which of the following is a property of the standard normal distribution?

Water Usage Narrative The mayor of the city of Windsor was informed that household water usage is a normally distributed random variable with a mean of 95 litres and a standard deviation of 16 litres per day. -Refer to Water Usage Narrative. If the mayor wants to give a tax rebate to the 20% lowest water users, what should the litres-per-day cut-off be?

Pacific Salmon Narrative The owner of a fish market determined that the average weight for a Pacific salmon is 3.6 kg, with a standard deviation of 0.8 kg. Assume the weights of the salmon are normally distributed. -Refer to Pacific Salmon Narrative. What is the probability that a randomly selected salmon will weigh more than 4.8 kg?

Braking Distance Narrative For a car travelling 60 kilometres per hour (km/h), the distance required to brake to a stop is normally distributed, with mean of 17 metres and a standard deviation of 2.4 metres. Suppose you are traveling 60 km/h in a residential area and a car moves abruptly into your path at a distance of 20 m. -Refer to Braking Distance Narrative. If you apply your brakes, what is the probability that you will brake to a stop within 14 m or less?

All binomial distributions can be approximated very closely by normal distributions.

A firm with many travelling salespersons decides to check the salespersons' travel expenses to see if they are correctly reported. An auditor for the firm selects 200 expense reports at random to audit. What is the probability more than 20% of the sampled reports will be incorrect when, in fact, only 10% of the firm's expense reports are improperly documented?

Bike Racks Assembly Time Narrative A manufacturer of bike racks for cars claims that the assembly time x for a particular model is normally distributed, with a mean of 1 hour and a standard deviation of 0.10 hours. -Refer to Bike Racks Assembly Time Narrative. Find the assembly time that exceeds 97.5% of all other assembly times for bike racks of this model.

College Applicants Narrative The admissions office of a community college in Ontario is asked to accept deposits from a number of qualified prospective freshmen so that, with probability of about 0.95, the size of the freshmen class will be less than or equal to 150. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the freshmen class if accepted. -Refer to College Applicants Narrative. How many deposits should the admissions counselor accept?

If x denotes a continuous random variable, then P(x = c) = 0 for every number c.