Question

about 20% of the population experiences \cybersickness.\ this happens when the images in 3 - d movies look so real they hinder the brains ability to sort signals and cause people to get nauseated. to find out if this applies to teens, an srs of 30 high school students was asked if they experience cybersickness. eight students said \yes.\ to see if this result is surprising, a simulation is conducted to estimate the probability of obtaining a sample result as high as this.
let 0 - 1 represent \yes\ and 2 - 9 represent
o.\
42188 55736 50953 82496 41985 07738
using the line of random numbers, how many \yes\ responses will there be in the first trial of the simulation?
2
4
15
26

Explanation:

Step1: Analyze each digit in the first number

The first number is \(42188\). We check each digit:

• The first digit \(4\) (represents "No" as \(4\in[2 - 9]\))
• The second digit \(2\) (represents "No" as \(2\in[2 - 9]\))
• The third digit \(1\) (represents "Yes" as \(1\in[0 - 1]\))
• The fourth digit \(8\) (represents "No" as \(8\in[2 - 9]\))
• The fifth digit \(8\) (represents "No" as \(8\in[2 - 9]\))

Step2: Count the number of "Yes" responses

From the analysis in Step1, there is \(1\) "Yes" response in the first number. But wait, we need to consider the entire trial. Wait, no, the problem is about the first trial. Wait, actually, each number in the line is a group of digits. Wait, no, the sample size is \(n = 30\). But in the simulation setup, each digit is a response. Wait, no, the numbers are grouped as \(42188\), \(55736\), \(50953\), \(82496\), \(41985\), \(07738\). But for a sample of \(n=30\), we need \(30\) digits. But the first trial (first set of digits). Wait, no, actually, each digit in the random - number sequence is a response. The first trial (using the first \(30\) digits). But looking at the first number \(42188\):

• For \(42188\): digits are \(4\), \(2\), \(1\), \(8\), \(8\). The digit \(1\) is a "Yes" (count \(1\))
• For \(55736\): digits \(5\), \(5\), \(7\), \(3\), \(6\) (all "No")
• For \(50953\): digit \(0\) is a "Yes" (count \(2\)), and digits \(5\), \(9\), \(5\), \(3\) are "No"
• For \(82496\): all digits \(8\), \(2\), \(4\), \(9\), \(6\) are "No"
• For \(41985\): digit \(1\) is a "Yes" (count \(3\)), and digits \(4\), \(9\), \(8\), \(5\) are "No"
• For \(07738\): digit \(0\) is a "Yes" (count \(4\)), and digits \(7\), \(7\), \(3\), \(8\) are "No"

Answer:

\(4\)