Exam 6: The Normal Probability Distribution

Which of the following distributions is considered to be the cornerstone distribution of statistical inference?

Continuous random variables can assume infinitely many values corresponding to points on a line interval.

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 less than 3.2 kg?

If Z is a standard normal random variable, then which of these values is P(-1.75 Z -1.25)?

If the random variable X is normally distributed, with a mean of 75 and a standard deviation of 8, which of the following values is the probability that X is greater than or equal to 75?

Which of the following is a valid statement about the mean, median, and mode?

Let x denote a normal random variable with mean 30 and standard deviation 5. What x-value is the 67th percentile of this distribution?

Let be a z-score that is unknown but identifiable by position and area. If the area to the right of is 0.8849, the value of is 1.2.

Many different types of continuous random variables give rise to a large variety of probability density functions. Which of those listed below are generated by such variables?

The normal probability distribution is right-skewed for large values of the standard deviation , and left-skewed for small values of .

A car dealership has found that the length of time before a major repair is required on the new cars it sells is normally distributed, with a mean of 36 months and a standard deviation of 9 months. If the dealer wants only 5% of the cars to fail before the end of the warranty period, for how many months should the cars be guaranteed?

If Z is a standard normal random variable, then the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?

The mean and standard deviation of a normally distributed random variable, which has been "standardized," are 1 and 0, respectively.

Given that Z is a standard normal random variable, which of the following is the value of P(-1.0 Z 1.5)?

x is a normally distributed random variable with a mean of 8.20 and variance of 4.41, and P(x > b) = 0.08. What is the value of b?

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

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. The mayor advertised on a local TV channel for about 3 weeks his intention to give a tax rebate to the 20% lowest water users. If the advertisement lowered the mean usage of 95 litres to 87 litres, what should the adjusted litres-per-day cut-off be?

The left half of the normal curve is slightly smaller than the right half.

Canada Revenue Agency Audits Narrative How does Canada Revenue Agency decide on the percentage of income tax returns to audit for each province? Suppose the Agency does it by randomly selecting 50 values from a normal distribution with a mean equal to 1.25% and a standard deviation equal to 0.4%. -Refer to Canada Revenue Agency Audits Narrative. What is the probability that a particular province will have more than 2% of its income tax returns audited?

Given a normal random variable x with mean and standard deviation , the mean of the standard normal random variable z associated with x is 1.