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: (a)  x = 260.52(b)  x = 249.24 (c)  x = 265.22 (d)  x = 297.65       Step-by-step explanation:Here,   Mean = [tex]\mu[/tex] = 300 Standard deviation = [tex]\sigma[/tex] = 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