Question

A standardized exam's scores are normally distributed In a recent year, the mean test score was 1495 and the standard deviation was 315. The test scores of four students selected at random are 1900, 1240, 2230, and 1400 Find the z-scores that correspond to each value and determine whether any of the values are unusual The z-score for 1900 is (Round to two decimal places as needed) The Z-score for 1240 is (Round to two decimal places as needed.) The z-score for 2230 is (Round to two decimal places as needed.) The z-score for 1400 is [] (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fillin the answer box within your choice 0 A. The unusual value(s) isare | (Use a comma to separate answers as needed.) O B. None of the values are unusual.

Answer 1

(a)

$\mu$ = 1495

$\sigma$ = 315

(i)

X = 1900

Z = (X - $\mu$ )/ $\sigma$

= (1900 - 1495)/315 = 1.29

So,

Answer is:

1.29

  (ii)

X = 1240

Z = (X - $\mu$ )/ $\sigma$

= (1240 - 1495)/315 = - 0.81

So,

Answer is:

- 0.81

  (iii)

X = 2230

Z = (X - $\mu$ )/ $\sigma$

= (2230 - 1495)/315 =2.33

So,

Answer is:

2.33

  (iv)

X = 1400

Z = (X - $\mu$ )/ $\sigma$

= (1400 - 1495)/315 = - 0.30

So,

Answer is:

- 0.30

  (b)

Correct option:

A. The unusual value is: 2230

EXPLANATION: X = 2230 has Z score = 2.33 > 2, i.e., X is more than 2 standard deviation from mean.

(c)

Cumulative area = 0.0072

Since the cumulative area is less than 0.5, Z lies on LHS of mid value and is negative.

Standard Normal Table gives Z score corresponding to area = 0.0072 as Z = - 2.445

So

Answer is:

- 2.445