Question

4. If the random variable X is normally distributed with mean = 4 and variance o2 = 2, find the values 2o such that a.) P(SX 330) = 0.4770 b.) PICOS X < 5) = 0.3770

Answer 1

Mean = 4

Standard deviation = sqrt variance = sqrt 2 = 1.4

(a) for x = 1

Z = 1-4/1.4 = - 2.14

The value for this z score according to z score table is 0.0162

Now, we know that to calculate the value for the x0, we will

Z score for x0 - z score for 1 = 0.4770

Value for Required z score - value of z score for - 2.14 = 0.4770

Value for Required z score - 0.0162 = 0.4770

Value for Required z score = 0.4770 + 0.0162

Value for Required z score = 0.4932

The z score is 0.02

For x = x0

Z = x0 - 4/1.4 = 0.02

0.02 = x0 - 4/1.4

0.028 = x0 - 4

X0 = 4.028​​​​​​

Similarly for (b) I'll do it shortly same as this

(b) P( x, 2 x2 5) = 0, 3770 хо- ч 2 х с 5-4 - о: 3170 1,4 іч эса — у 4 с 4 ) p. 3770 1 ч 1, ч Ха-ч 4 ) 2 o-11 = 0. 3770 1 ч хо-Ч 4 х 4 р. 7 1 2 б. 3770 (ч о. 7611 - Хо – 4 = 0:317о |: Ч o-16L - о. 3770 = До -ч Со -4 -7 (0- 384) 1 ч

Now, the z score for the value of 0.3841 is - 0.29

X0 - 4/1.4 = - 0.29

X0 - 4 = - 0.406

X0 = 3.594