Question

answer questions 9 &10. Consider the continuous random variable defined by f(x) information to tvald over the intervai 1 s x s 3. that i Determine P(1 sX s 2.5) . (2 Points) 10. (2 Points) Calculate ECX) Use the following information to answer questions 11-13. Tool life for a machining operation is given as the number of parts produced before a tool is replaced. Tool life follows a normal distribution with a mean of 85 and standard deviation of 3. Calculate the requested probabilities. 11. (2 Points) What is the probability that a tool produces at least 82 pcs? 12. (2 Points) What is the probability that a tool produces more than 86 pcs? 13. (2 Points) What tool life corresponds to the 90h percentile? Cs Scanned with CamScanner

Answer 1

(9)

2.5 0.05 × x3d2. P(1 < X < 2.5)

= 0.05 ×--

between the limits 1 to 2.5.

Applying limits, we get:

P(1 < X < 2.5) 0.4883-0.0125-0.4758

So,

Answer is:

0.4758

(10)

0.05 × 14 dr E(X) =

= 0.05 ×

between the limits 1 to 3.

Applying limits, we get:

E(X) = 2.43-0.01 = 2.42

So,

Answer is:

2.42

(11)

$\mu$ = 85

$\sigma$ = 3

To find P(X$\geq$82):

Z = (82 - 85)/3

= - 1.00

Table of Area Under Standard Normal Curve gives area = 0.3413

So,

P(X$\geq$82) = 0.5 + 0.3413 = 0.8413

So,

Answer is:

0.8413

(12)

To find P(X>86):

Z = (86 - 85)/3

= 0.3333

Table gives area = 0.1293

So,

P(X>86)= 0.5 - 0.1293 = 0.3707

So,

Answer is:

0.3707

(13)

90th percentile corresponds to area 0.90 - 0.50 = 0.40 from mid value to Z on RHS.

Table gives Z = 1.28

So,

Z = 1.28 = (X - 85)/3

So,

X = 85 + (1.28 X3)

   = 88.84

So,

Answer is:

88.84