Question

Gru's schemes have a/an 9% chance of succeeding. An agent of the Anti-Villain League obtains access to a simple random sample of 1100 of Gru's upcoming schemes.
Find the probability that...
(Answers should be to four places after the decimal, using chart method, do NOT use the continuity correction):

...between 95 and 101 schemes will succeed:

...less than 8.5% of schemes will succeed:

...more than 9.5% of schemes will succeed:

...between 8.5% and 9.5% of schemes will succeed:

Answer 1

(a)

n = 1100

p = 0.09

q = 1 -p = 0.91

To fond P(95 < X < 101):
For X = 95:
Z = (95 - 99)/9.4916

= - 0.4214

By Technology, Cumulative Area Under Standard Normal Curve = 0.3367

For X = 101:
Z = (101 - 99)/9.4916

= 0.2107

By Technology, Cumulative Area Under Standard Normal Curve = 0.5834

So

P(95 < X < 101):= 0.5834 - 0.3367 = 0.2467

So,

Answer is:

0.2467

(b)

n = 1100

p = 0.09

q = 1 - p = 0.91

SE =

To find P( < 0.085):

Z = (0.085 - 0.09)/0.008629

= - 0.5794

By Technology, Cumulative Area Under Standard Normal Curve = 0.2812

So,

P(<0.085):=0.2812

So,

Answer is:

0.2812

(c)

n = 1100

p = 0.09

q = 1 - p = 0.91

SE =

To find P( > 0.095):

Z = (0.095 - 0.09)/0.008629

= 0.5794

By Technology, Cumulative Area Under Standard Normal Curve = 0.7188

So,

P( > 0.095) = 1 - 0.7188 = 0.2812

So,

Answer is:

0.2812

(d)

n = 1100

p = 0.09

q = 1 - p = 0.91

SE =

To find P(0.085 < < 0.095):

For = 0.085:

Z = (0.085 - 0.09)/0.008629

= - 0.5794

By Technology, Cumulative Area Under Standard Normal Curve = 0.2812

For = 0.095:

Z = (0.095 - 0.09)/0.008629

= 0.5794

By Technology, Cumulative Area Under Standard Normal Curve = 0.7188

So,

P(0.085 < < 0.095):= 0.7188 - 0.2812 = 0.4376

So,

Answer is:

0.4376