Answered

. Find each of the following probabilities for a normal distribution. a. p(21.80 , z , 0.20) b. p(20.40 , z , 1.40) c. p(0.25 , z , 1.25) d. p(20.90 , z , 20.60)

Sagot :

Correct question is;

A. p(-1.80 < z < 0.20 )

B. p(-0.4 < z < 1.4)

C. p(0.25 < z < 1.25)

D. p(-0.9 < z < -0.6)

Answer:

A) p(-1.80 < z < 0.20) = 0.54333

B) p(-0.4 < z < 1.4) = 0.57466

C) p(0.25 < z < 1.25) = 0.29564

D) p(-0.9 < z < -0.6) = 0.90981

Step-by-step explanation:

A) p(-1.80 < z < 0.20 )

This gives us;

P(z < 0.2) - P(z < -1.8)

From z-distribution tables;

P(z > 0.2) = 0.57926

And P(z < -1.8) = 0.03593

Thus;

p(-1.80 < z < 0.20) = 0.57926 - 0.03593 p(-1.80 < z < 0.20) = 0.54333

B) p(-0.4 < z < 1.4)

This gives us;

P(z < 1.4) - P(z < -0.4)

From z-distribution table, we have;

P(z > 1.4) = 0.91924

P(z < -0.4) = 0.34458

Thus;

p(-0.4 < z < 1.4) = 0.91924 - 0.34458

p(-0.4 < z < 1.4) = 0.57466

C) p(0.25 < z < 1.25)

From z-distribution table, we have;

P(z < 0.25) = 0.59871

P(z > 1.25) = 0.10565

Now, to solve this;

p(0.25 < z < 1.25) = 1 - (P(z < 0.25) + P(z > 1.25))

This gives;

p(0.25 < z < 1.25) = 1 - (0.59871 + 0.10565)

p(0.25 < z < 1.25) = 0.29564

D) p(-0.9 < z < -0.6)

From z-distribution table, we have;

P(z < -0.9) = 0.18406

P(z > -0.6) = 0.72575

Thus;

p(-0.9 < z < -0.6) = 0.18406 + 0.72575

p(-0.9 < z < -0.6) = 0.90981