![]() This corresponds with a cumulative probability of P(z<3.40) = 0.99966. We still need to consult the probability for 6.5 minutes, following the same procedure: We know the probability for 5.6 minutes from former answers (P(z<1.60) = 0.94520. ![]() The probability that calls last between 5.6 and 6.5 minutes As a result, consulting the associated probability for each z-score in the cumulative standard normal table, we have:įor z = 0, P(z5.6) = P(z>1.60) = 1 - P(z<1.60) = 1 - 0.94520 = 0.0548 (four decimal places).3. The probability between 4.8 and 5.6 minutes is the resulting difference between these two values. The corresponding z-scores for 4.8 minutes and 5.6 minutes are respectively:Īs we can see, the z-score for a raw value of 4.8 coincides with the population mean, thus the z-score = 0. The probability that calls last between 4.8 and 5.6 minutes We also need to have into account that the normal distribution is symmetrical, an indispensable property to calculate negative z-scores, that is, values below the population mean.1. We have a normal distribution with known parameters, that is, for the population mean and for the population standard deviation:įor each of the questions, we have to transform either raw score to a z-score as a way to use the cumulative standard normal distribution table for consulting the probabilities values for each z-score.
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