Normal distributions, however, deal with continuous variables which are endless in the number of times you can divide their intervals, such as gross pay, heights, or cholesterol levels. RULE: If np > 5 and n(1 - p) > 5, the normal curve will be a good approximation for the binomial distribution (usually good to two or three decimal places).īinomial distributions deal with discrete variables which are made of whole units with no values between them, such as coin flips that are heads or tails, basketball tosses that make the hoop or not, or machine parts that are defective or not. When the number of expected successes and failures is sufficiently large, an area under the normal curve will be a good numerical approximation of the exact binomial computation. The closer p is to 0.5 and the larger the number of trials, n, the more symmetric the distribution becomes. When p is not equal to 0.5, the binomial distribution will not be symmetric. The probability that an outcome is less than d equals the area under the normal curve bounded by d and negative infinity (as shaded in the diagram at the right).īinomial distributions where p = 0.5 (such as this coin flipping example) are symmetric. ![]() On the normal distribution curve, the probability that an outcome is greater than d equals the area under the normal curve bounded by d and positive infinity. A normal distribution is really a continuous probability distribution. The situation is such that as the number of tosses increases, the better the fit to the normal curve. The super-imposed curve represents a normal distribution curve approximation for this binomial distribution. The vertical bars represent the probabilities of obtaining each of the possible 21 outcomes (0 - 20 heads). Statistician Abraham de Moivre (18 th century) discovered that as the number of coin flips increased, the shape of the binomial distribution approached a very smooth curve. See the binomial distribution for 20 flips below, with a superimposed curve. You can run this program now by building it ( /B), saving it ( /S), adding a new page ( / ~) and typing Coins() and hitting enter.In the Binomial Probability lesson, we saw the binomial distributions for 2 flips and 4 flips of a fair coin. The last line uses the Disp command to display the result of the coin flip. Remember, to store a result in a variable you have to use STO command ( /h) for that little arrow →. The letter “s” was used for the variable because “s” is often used to represent a string (text) variable. If you are using the TI-Nspire Student Software on a computer you might want to type “Heads” and “Tails” instead of “H” & “T.” This example used just the letters “H” and “T” for “Heads” and “Tails” so that you do not have to type so much on the goofy keyboard. If randInt(1,2)=1 Then © remember, If…Then…Else…EndIf is b 4 3 Here is one way to write that in TI-Basic: ![]() In this example, we will use “1 means heads and 2 means tails.” You might say, “ If the random number is 1, we have heads, otherwise (else) we have tails.”Īre you starting to think like a computer programmer yet? Once we have our random number, 1 or 2, we have to decide what 1 and 2 mean. So we will use RandInt(1,2), which asks the calculator to give you back a random number that is at least 1 but not more than 2. Because there are two possible outcomes, heads or tails, we want the RandInt() function to return back only two numbers, 1 and 2. You will need to use the RandInt() function to pretend to flip a coin. Just understanding how to get the calculator to flip a coin is going to take a little thinking.
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