Let the continuous random variable X denote the distance in micrometers from the start of a track on a magnetic disk until the first flaw. Historical data show that the distribution of X can be modeled by a pdf: 1 f (x) = x > 0 2000 2000 For what proportion of disks is the distance to the first flaw greater than 1,418 micrometers?

Suppose that X follows a lognormal distribution with w^2=4 and E(X)=10,000 a. Find the parameter theta for the distribution. Use 4 digits after the decimal point: b. Find the standard deviation of the process: Use 4 digits after the decimal point:

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 99, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 99. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value -1 -1.5 0 +). Click and drag the arrows to adjust the values. 1 2 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement. Edit Insert Formats B I U x₂ x² A => EM e & N 18 (f) The middle 50% of IQs fall between what two values? (g) Sketch the graph and write the probability statement. Edit Insert Formats BIUX₂ X² A E = = E EC P R N • Σ+ Σ Α Σ+ Σ Α

A certain variable has a bell-shaped distribution with mean μ=176.16μ=176.16 and standard deviation σ=4.9σ=4.9. You observe a value of x=184x=184. Is this a TYPICAL value of the variable (within 2 standard deviations of the mean), or an UNUSUAL one (more than 2 standard deviations from the mean)?

Suppose the average life of kiwi phones is 4.66 years with standard deviation 1.05 years. Let X represent the average lif of 40 r/s kiwi phones. Find P( x > 5)