Question

Find the value of z such that 0.9426 of the area lies between −z−z and z. Round your answer to two decimal places.

Answer 1

The z-score is the number of standard deviations away from the mean that a data point is. To find the value of z for which 0.9426 of values are within z deviations of the mean, this means that (1 - 0.9426) = 0.0584 are beyond this interval, and this would be divided by 2: 0.0584 / 2 = 0.0292 of values are located below -z, while another 0.0292 is above +z.
Based on z-tables, this occurs at around z = 1.89, so the interval is from -1.89 to 1.89.

Answer 2

The value of z is $1.89$.

Z score also called standard score which given you an idea of how far from the mean a data point is.

The absolute value of z represents the distance between that raw score x and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above.

The value of $z$ for which $0.9426$ of values are within the deviations of mean i.e,

$1-0.9426$ are beyond interval and further

$Deviation\; from\; the\; mean = \dfrac{1-0.9426}{2}$ of values are located below $-z$ while another $\dfrac{1-0.9426}{2}$ is above $z$.

So in z-tables, this occurs at $z=1.89$.

Learn more about z-tables here;

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