Answers

1. 0.7734 or 77.34 %

   • We can convert any normal distribution to a normal distribution  to find the probabilities and apply the properties of the  normal. To do this, we use the z score.

   • The Z value (or sometimes called the Z-score or simply Z) represents the number of standard deviations between an observation and the mean of a data set.

   • For any normal random variable, if you find a Z-score for a value (i.e. normalize the value), the random variable will be transformed into a standard random variable and you can find the probability by using  standard tables.

   If the area under the standard curve to the right of the z-value is 0.75, then the area under the curve to the left of that z-value is 0.25.

   Using the normal table (z), find 0.2500 of the probabilities. The closest zone to 0.2500 is 0.2514. The z value associated with this is -0.67.

   The probability that a randomly selected z is greater than -0.67 is about 0.75.

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2. Answer:

   0.7734 or 77.34 percent

   Step-by-step explanation:

   If the area under the Standard Normal curve to the right of a z value is 0.75, then the area under the curve to the left of that z value is 0.25. Using a Standard Normal (z) table, look up 0.2500 among the probabilities. The area closest to 0.2500 is 0.2514. The z value associated with this is -0.67.

   The probability of a randomly selected z is greater than -0.67 is approximately 0.75.

   A z-score measures exactly how many standard deviations above or below the mean a data point is.

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