Find x such that P(X ≤ x) = 0.350. (Statistics with a Z Table)

Question

Hi I am looking to find the steps to solve this probability question.

Let X be normally distributed with mean μ = 132 and standard deviation σ = 35. [You may find it useful to reference the z table.]

Find x such that P(X ≤ x) = 0.350. (Statistics with a Z Table)

Answer 1

The answer above is incorrect.

If you look up 0.35 in the body of the table you find it in row -0.3 and column 0.08. So the correct Z value is

-0.39 or -0.385 if you interpolate then you can use the formula

X = mean + Z * stdev X = 132 + (-0.39*35) = 118.35

OR you can use the invNORM function on a TI-83, TI-84 or TINspire

invNORM(area left of x, mean, stdev) returns x invNORM(0.35,132,35) which returns 118.51

the small difference in answers is due to rounding.

Answer 2

Mary,

From the Z-table, you can look for a z-value for which the corresponding cumulative probability ( which means the area to the left of Z).

In the table, when row value is -0.3 and column value is 0.08,

z = -0.3 +0.08 = -0.22 and cumulative probability is 0.3520

Similarly, when the row value is -0.3 and column value is 0.09,

z = -0.3 +0.09 = -0.21 and cumulative probability is 0.3483.

Pick the value of z for which the cumulative probability is closest to 0.35. Hence, z = -0.21.

z and x are related by the equation, x = μ + zσ

Therefore x = 132 + (-0.21× 35) = 124.65