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The binomial probability formula can be used to find the probability of a binomial experiment for a specific number of successes.  It DOES NOT find the probability for a RANGE of successes, as in this case.   The RANGE "x≤4" means x=0 OR x=1 OR x=2 OR x=3 OR x=4, so there...

First, is the distribution of the sample approximately normal? Yes, n=100 makes this a good approximation even if the population distribution is only slightly bell shaped.   The standard error of a proportion of a sample is given by √(p*q/n) = √[(.2)(.8)/100] = .04.   A...

By definition the mean is the "balance point" of the probability. A score above the mean has exactly the same probability as a score above the mean. So the probability of a score being less than the mean and the probability of a score being above the mean are the same: 50 percent or 0...

The point of this problem is to decide whether the distribution of the sample mean is approximately normal. If it is then we can estimate the probability using the z-score formula and the probability tables for the standard normal distribution.   The big question is whether this is...

1) Calculate a z score for the value 120   z = (x-μ)/σ = (120-109)/12 = 11/12 = .9167   The p-value for P(Z<.9167) = .8204, but we need to find P(Z>.9167) so 1 - .8204 = .1796; roughly 18 percent.   2) The phrase "top 10 percent" means the area...

The proportion of wardens who think tattoos are a sign of trouble is the number of wardens who think tattoos are a sign of trouble divided by the sample size, 98/212 = 0.4623.   Hº: The proportion of wardens who feel that tattoos are a sign of trouble is ≥ 0.5 Hª: The...

You need to calculate two z-scores, one for each of the values 62.5 and 67.7, using the formula z = (x-μ)/σ.   z1 = (62.5-64.3)/1.15 = -1.56 z2 = (67.7-64.3)/1.15 = 2.96   Convert each z-score to a probability (also called a p-value) using a probability table or calculator...

Let's do some trial and error and see what we can learn.   If there are 5 scores and the mean is 8 then (? + ? + ? + ? + ?)/5 =8. Multiple both sides of the equation by 5 and we get (? + ? + ? + ? + ?) = 40, that is, the sum of the scores is...

The key to solving this type of problem is to understand that we're being given two different types of numbers here: the count of coins versus the value of the coins.   Let's work with the count of coins first: there are four more quarters than dimes. (For example, if we have 4 dimes...

A standing wave occurs when the frequency of the oscillator and the frequency of the string are the same.    A wave travels along a string at a constant speed so it takes more time to travel a longer distance. This changes the frequency of the string and therefore it will no longer...

It's hard to help with this without giving away the game.   Consider the graph of the absolute value of x. It has a vee shape. When x is positive it's a line with slope of +1 and y-intercept of 0. When x is negative it's a line with a slope of -1 and y-intercept of 0. Get some graph...

Hello Craig, For the trigonometric functions sin and cos the constants in the equation determine the magnitude, frequency and phase. For the equation y = 3 * sin( pi*x + pi/2) the amplitude is 3, the frequency is pi and the phase shift is 1/2. A generalized equation would be: (Eq...

Can you describe the composite figure for us? There really isn't enough information to find a solution without making some assumptions. Perhaps this is a cylindrical container with a bottom but no top?

If we consider each side of the equation separately we see that they each represent straight lines in the form y=mx+b (the slope-intercept form). The equation y=3x+14 is a line with slope of 3 and y-intercept of 14. The equation y=3x is a line with slope of 3 and y-intercept of 0. These...

Hi Destiny! The first step is to determine where the ten-thousands place is. Most people 'count' the digits from right to left starting at the decimal point: "ones", "tens", "hundreds", "thousands", "ten thousands" -- five places left of the...