Question

For a standard normal distribution, find the approximate value of mc005-1.jpg. Use the portion of the standard normal table below to help answer the question.

Answer 1

Thank you for asking this question. The question seems to be incomplete:

Here is the complete question:

For a standard normal distribution, find the approximate value of P(-0.78 = z = 1.16). Use the portion of the standard normal table below to help answer the question.

(z)

0.00

0.16

0.22

0.78

1.00

1.16

1.78

2.00

(Probabilities)

0.5000

0.5636

0.5871

0.7823

0.8413

0.8770

0.9625

0.9772

Answer:

Ф(1.16) = 0.8770

Ф(0.78)=0.7823

We know that the curve is symmetrical Ф(-0.78)=1-0.7823=0.2177

P(-0.78 < z < 1.16) = Ф(1.16)-Ф(-0.78)

= 0.8770-0.2177

= 0.6593

The final answer for this question is:  0.6593

If there is any confusion please leave a comment below.

Answer 2

Answer: B. 66%

From the given table,

Ф (1.16) = 0.8770; and

Ф (0.78) = 0.7823;

For a symmetrical curve,

Ф (-0.78) = 1- 0.7823 = 0.2177;

Thus,

P (-0.78 ≤ z ≤ 1.16) = Ф (1.16) – Ф (-0.78)

On substitution,

= 0.8770 - 0.2177;

= 0.6593

Therefore, the probability is 0.6593.

Then converting the obtained value into the corresponding percentage will be 66 % (approximately).