Question

A survey of 2,350 adults reported that 55% watch news videos. Complete parts​ (a) through​ (c) below

Suppose that you take a sample of 50 adults. If the population proportion of adults who watch news videos is 0.55 what is the probability that fewer than half in your sample will watch news​ videos?

The probability is what? that fewer than half of the adults in the sample will watch news videos

The probability is what % that fewer than half of the adults in the sample will watch news videos.

Answer 1

Given : P = 0.55 , n = 50

Therefore Mean ( µ ) = n*p = 27.5 and standard deviation (σ) = =  3.5178

We are asked to find P( x < 25 )

First we need to use continuity correction by subtracting 0.5 from 25

P( x < 25 -0.5 ) = P( x ≤ 24.5 )

P( x ≤ 24.5 ) =

= P( z ≤ -0.85 )

= 0.1977

The probability that fewer than half of the adults in the sample will watch news videos is 0.1977 or 19.77%