Exam 6: The Normal Probability Distribution

The mean and variance of any normal distribution are always 0 and 1, respectively.

Given a normal random variable x with mean of 70 and standard deviation of 12, the value of the standard normal random variable z associated with x = 82 is larger than 0.

If the random variable x is normally distributed with a mean of 88 and a standard deviation of 12, what is the value of P(x 96)?

University Faculty Survey Narrative A recent survey of university faculty reported 55% were considering going into another profession. -Refer to University Faculty Survey Narrative. What is the approximate probability 60 or more faculty from a random sample of 200 would be considering going into another profession?

Suppose z has a standard normal distribution. Then below which value do 28.1% of the possible z-values occur?

Eligible Manitoba Voters Narrative Past records indicate 60% of the eligible voters in Manitoba vote in local elections. -Refer to Eligible Manitoba Voters Narrative. What is the expected number in a random sample of 200 eligible voters who will vote in the next local election?

Loans Narrative Historical data collected at a small bank in Nova Scotia revealed that 80% of all customers applying for a loan are accepted. Suppose that 50 new loan applications are selected at random. -Refer to Loans Narrative. What is the probability that at least 42 loans will be accepted?

Transport Canada studies of fuel consumption indicate compact car fuel consumption to be normally distributed with a mean of 8.5 litres per 100 km and a standard deviation of 1.5 L/100 km. What percentage of compact cars use between 6.8 and 12.0 L/100 km?

The time it takes Jessica to bicycle to school is normally distributed, with a mean time of 15 minutes and a variance of 4 minutes. Jessica has to be at school at 8:00 A.m. Suppose it took her 23 minutes to get to school. What can you reasonably infer or conclude?

U.S. Presidential Election Narrative Do Americans tend to vote for the taller of the two candidates in a presidential election? In 30 presidential elections since 1856, 18 of the winners were taller than their opponents. Assume that Americans are not biased by a candidate's height and that the winner is just as likely to be taller or shorter than his opponent. Is the observed number of taller winners in the U.S. presidential elections unusual? -Refer to U.S. Presidential Election Narrative. Find the approximate probability of finding 18 or more of the 30 pairs in which the taller candidate wins.

A normal random variable x has mean 36.7 and standard deviation 10. Find a value of x such that the area under the normal distribution to the right of this value is equal to 0.01.

What proportion of the data from a normal distribution is within two standard deviations from the mean?

Even though the normal probability distribution deals with continuous variables, under certain circumstances we can use it to approximate various discrete probability distributions. Under which of these conditions is the use of the normal probability distribution permissible?

Using the standard normal curve, the z-score representing the 95th percentile is 1.645.

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 is the 95th percentile of this normal distribution?

Suppose x is normally distributed, with a mean of 75 and a standard deviation of 4. Would it be unusual to observe a value x = 59?

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. Find the probability that a randomly chosen household uses more than 87 litres per day.

A normal random variable x has an unknown mean and a standard deviation . If the probability that x exceeds 7.5 is 0.8289, find

Eligible Manitoba Voters Narrative Past records indicate 60% of the eligible voters in Manitoba vote in local elections. -Refer to Eligible Manitoba Voters Narrative. is the approximate probability more than 150 from a sample of 200 will vote in the next local election?

Which of these statements is valid with regard to probabilities of continuous random variables?