A coin was flipped 16 times and came up heads 13 times a The

A coin was flipped 16 times and came up heads 13 times (a) The assumption of normality is justified O Yes O No (b-1) Calculate a p-value for the observed sample outcome, using the normal distribution. (Round your z- value to two decimal places. Round your answer to 4 decimal places.) p-value (b-2) At the 0.05 level of significance in a right-tailed test, is the coin biased toward heads? O Yes O No (c) Use Excel to calculate the binomial probability P(X213 In 16, m -0.50) 1 P(X s 12 INE 16, 0.50). (Round your answer to 4 decimal places.) P(X2 13) (d)The normal probability is O The same as the binomial probability O An approximation

Solution

a).

n=16

p=0.5

np=8, n(1-p) =8 both > 5

The assumption is justified.

Answer: A yes

b1).

Expectation = np = 8

Variance = np(1 - p) = 4

Standard deviation = 2

x=13

z value for 12.5, z=(12.5-8)/2 = 2.25

z value for 13.5, z=(13.5-8)/2 = 2.75

P( x=13)= P( 2.25<z<2.75)

= P( z <2.75) – P( z<2.25)

=0.9970- 0.9878

=0.0092

b2).  

Answer: Yes    ( because calculated 0.0092 < 0.05)

c).

P( x >=13 ) = 0.0106

d).

Normal probability is

An approximation