Exam 6: The Normal Probability Distribution

Suppose that the z-value for a given value x of the random variable X is z = 1.96, and that the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6. To what x-value does this z-value correspond?

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if which of the following conditions holds?

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 10 or fewer are Rh-negative?

A continuous random variable x is normally distributed with a mean of 1200 and a standard deviation of 150. Given that x = 1410, its corresponding z-score is 1.40.

A continuous random variable x is normally distributed with a mean of 100 km and a standard deviation of 20 km. Given that x = 120, its corresponding z-score is -1.0.

Given that Z is a standard normal random variable, what is P(-1.2 Z 1.5)?

A certain type of automobile battery is known to have a lifespan that is normally distributed, with mean 1100 days and standard deviation 80 days. For how long should these batteries be guaranteed if the manufacturer wants to replace only 5% of the batteries sold because they "died" before the guarantee expired?

Soup Cans Narrative The liquid volumes contained in cans of soup produced by a company are normally distributed, with a mean of 425 mL and a standard deviation of 16 mL. -Refer to Soup Cans Narrative. Determine the minimum volume of the fullest 5% of all cans of soup produced.

The normal probability distribution is one of the most commonly used discrete probability distributions.

Let be a z-score that is unknown but identifiable by position and area. If the symmetrical area between - and + is 0.903, the value of is 1.66.

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 probability that it takes at most 1.1 hours to assemble a bike rack of this model.

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, which of these is the value of P(85 X 90)?

Given that X is a binomial random variable, then between which of the following values would the binomial probability P(X = x) be approximated by the area under a normal curve?

Adding or subtracting 0.5 from the binomial random variable x's interval endpoints (i.e., the so-called continuity correction) improves the normal approximation to the binomial by correcting for or accounting for the "missing" corners of the probability rectangles corresponding to values of x.

University Football Narrative A student government representative claims that 55% of the student body of a local university favour a move to Division I in university football. A random sample of 2000 students is selected. -Refer to University Football Narrative. What is the expected number of students that will favour the move to Division I?

Let x be a binomial random variable with n = 25 and p = 0.3. a. Is the normal approximation appropriate for this binomial random variable? b. Find the mean and standard deviation for x. c. Use the normal approximation to find d. How close was your approximation? d. Use the cumulative binomial probabilities table in Appendix 1 of the textbook to calculate the exact probability Compare the results of parts c and

Given that X is a binomial random variable, the binomial probability P(X x) is approximated by the area under a normal curve to the right of which of the following values?

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 the number of loans rejected is between 10 and 15, inclusive?

Salmon Flies Lifespan The lifetime of salmon flies is normally distributed, with a mean of 60 days and a standard deviation of 20 days. -Refer to Salmon Flies Lifespan paragraph. Find the value x₀ such that 6.3% of salmon flies live less than x₀ days.

Let be a z-score that is unknown but identifiable by position and area. If the symmetrical area between a negative and a positive is 0.8132, what would be the value of ?