Question

An SRS of 1500 US adults were asked whether they were concerned about the outbreak of a global pandemic. In fact, 35% of all adults were concerned about the outbreak. What is the probability that the poll will be within 3 percentage points of the true p?

Group of answer choices

0.896

0.985

0.105

0.015

Answer 1

Solution

Given that,

p = 0.35

1 - p = 1 - 0.35 = 0.65

n = 1500

= p = p = 0.35

  [p ( 1 - p ) / n] = [(0.35 * 0.65) / 1500 ] = 0.0123

P(0.32 < < 0.38 )

= P[(0.32 - 0.35) / 0.0123 < ( - ) / < (0.38 - 0.35) / 0.0123 ]

= P(-2.44 < z < 2.44 )

= P(z < 2.44) - P(z < -2.44)

Using z table,   

= 0.9927 - 0.0073

= 0.985