Question

In 100 tosses of a fair​ coin, let X be the number of heads. Estimate ​Pr(46less than or equalsXless than or equals58​). Use the table of areas under the standard normal curve given below.

​Pr(46less than or equals≤Xless than or equals≤585)equals=

Answer 1

n = 100

p = 0.5

q =0.5

= np = 100 X 0.5 = 50

=

To find P(46 X 58):
Case1: For X from 46 to mid value:

Applying Continuity Correction for Normal approximation, we get:

For X from 45.5 to mid value:

Z = (45.5 - 50)/5 = - 0.9

Table gives area = 0.3159

Case 2: For X from mid value to 58:

Applying Cotinuity correction for Normal approximation, we get:

For X from mid value to 58.5:
Z = (58.5 - 50)/5 = 1.7

Table gives area = 0.4554

So,

P(46 X 58) = 0.3159 + 0.4554 = 0.7713

So,

Answer is:

0.7713