Using the Normal Distribution

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The Normal Distribution

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Presentation transcript:

Using the Normal Distribution Nulake 6th form maths 1999 page 305

Using the Normal Distribution tables calculate the area under the standard normal curve for each of the following 0.5-0.2190 = 0.2810 P(Z < -0.58) P(-2.31 < Z < -1.67) P(Z > -1.871) P(-1.5 < Z < 1.5) P(Z > -0.596) P(-1.97 < Z < 0.425) -0.58 0 0.4896-0.4525 = 0.0371 -2.31 -1.67 0 0.5+0.4694 = 0.9694 -1.871 0 0.4332+0.4332 = 0.8664 -1.5 0 1.5 0.5+0.2245 = 0.7245 0.4756+0.1646 = 0.6402

The mean mark in a university stage one math exam was 51% with a standard deviation of 16%. Assuming the marks are normally distributed find the probability that a student selected at random scored Less than 55% If 250 students sat the math exam how many scored between 35 and 45%? To standardise we use Z = To find P(X < 55) standardising = P(Z < ) Simplifying = P(Z < 0.25) Using tables = 0.5 + 0.0987 = 0.5987 51 55 0 0.25

The mean mark in a university stage one math exam was 51% with a standard deviation of 16%. Assuming the marks are normally distributed find the probability that a student selected at random scored If 250 students sat the math exam how many scored between 35 and 45%? To find P(35 < X < 45) standardising = P( < Z < ) Simplifying = P(-1 < Z < -0.375) Using tables = 0.3413 - 0.1462 = 0.19517 Number of students = 0.19517 x 250 = 48 students (rounding down) -51 -51 35 45 51 -1 0 -0.375