Question

Terms 2 Questions 3 Scores on the Stanford-Rinst i test are assumed to be normally standard deviation of 15 10% of the population? testare assumed to be normally distributed with a mean of 100 and a wit percent of the portation score above 1257 Below what score lie the lowest l Question 4. A task consists of installing an electric harness under the dashboard of a General Motors car. Assume that the times for these tasks are normally distributed with a mean of eleven minutes and a standard deviation of two and a half minutes. If one task is observed, find the probability that it will fall between seven minutes and fifteen minutes.

Answer 1

3.

µ = 100, σ = 15

Percent of the population above 125, P(X > 125) =

= P( (X-µ)/σ > (125-100)/15)

= P(z > 1.6667)

= 1 - P(z < 1.6667)

Using excel function:

= 1 - NORM.S.DIST(1.6667, 1)

= 0.0478 = 4.78%

Lowest 10% of the population lie below:

P(x < a) = 0.1

Z score at p = 0.1 using excel = NORM.S.INV(0.1) =-1.28

Value of X = µ + z*σ = 100 + (-1.28)*15 = 80.8

--------------------

4. µ = 11, σ = 2.5

P(7 < X < 15) =

= P( (7-11)/2.5 < (X-µ)/σ < (15-11)/2.5 )

= P(-1.6 < z < 1.6)

= P(z < 1.6) - P(z < -1.6)

Using excel function:

= NORM.S.DIST(1.6, 1) - NORM.S.DIST(-1.6, 1)

= 0.8904

-------------------

5.

µ = 298, σ = 3

P(X < 295) =

= P( (X-µ)/σ < (295-298)/3 )

= P(z < -1)

Using excel function:

= NORM.S.DIST(-1, 1)

= 0.1587

--------------------

6.

µ = 4.64, σ = 0.25

Z score at p = 0.90 using excel = NORM.S.INV(0.90) = 1.28

Value of X = µ + z*σ = 4.64 + (1.28)*0.25 = 4.96