Question

Suppose you are working with a data set that is normally distributed, with a mean of 300 and a standard deviation of 47. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places.) (a) 80% of the values are greater than x. (b) x is less than 14% of the values. (c) 23% of the values are less than x. (d) x is greater than 52% of the values

Answer 1

Answer:

(a)  x = 260.52

(b)  x = 249.24

(c)  x = 265.22

(d)  x = 297.65      

Step-by-step explanation:

Here,  

Mean = $\mu$ = 300

Standard deviation = $\sigma$ = 47

(a)   Using standard normal table,

P(Z > z) = 80%

1 - P(Z < z) = 0.8

P(Z < z) = 1 - 0.8

P(Z < -0.52) = 0.2  

z = -0.84

Using z-score formula,

x = z × σ + μ

x = -0.84 × 47 + 300 = 260.52

(b)  Using standard normal table,

P(Z < z) = 14%

P(Z < -1.08) = 0.1 4

z = -1.08

Using z-score formula,

 x = z × σ + μ

x = -1.08 × 47 + 300 = 249.24

(c) Using standard normal table,

P(Z < z) = 23%

P(Z < -0.74) = 0.243

z = -0.714

Using z-score formula,

 x = z × σ + μ

x = -0.74 × 47 + 300 = 265.22

(d)  Using standard normal table,

P(Z > z) = 52%

1 - P(Z < z) = 0.52

P(Z < z) = 1 - 0.52

P(Z < -0.25) = 0.4 8

z = -0.05

Using z-score formula,

x = z × σ + μ

x = -0.05 × 47 + 300 = 297.65