Question

Suppose you are working with a data set that is normally distributed, with a mean of 350 and a standard deviation of 48. Determine the value of x from the following information.

a. 70% of the values are greater than x.
b. x is less than 10% of the values.
c. 24% of the values are less than x.
d. x is greater than 60% of the values.

Answer 1

324.848

288.464

316.112

337.856

Explanation:

Given that :

Mean (m) = 350

Standard deviation (σ) = 48

Determine the value of x for the following :

Using the z probability calculator :

a.) 70% of the values are greater than x.

1 - 0.7 = 0.3

P(x < 30%) = P(x < 0.3) = - 0.524 = z

Z = (x - m) / σ

x = (z * σ) + m

X = (- 0.524 * 48) + 350 = 324.848

b.) x is less than 10% of the values.

P(x < 0.1) = - 1.282 = z

X = (- 1.282 * 48) + 350 = 288.464

C.) 24% of the values are less than x

P(x < 0.24) = - 0.706 = z

X = (- 0.706 * 48) + 350 = 316.112

D.) x is greater than 60% of the values

P(x > 0.6) = -0.253 = z

X = (- 0.253 * 48) + 350 = 337.856