Question

homes using television (hut) at a particular time is one measure of viewing activity within the television audience in the united states of america. when multiplied with share, it creates rating. share is based on percentage of televisions viewing a particular program of all televisions in use during a particular period. rating, then, is a numerical representation of the percentage of all television - owning households during a particular time period who are viewing a specific program. the relationship is set up formulaically here to solve for rating.
rating = share × hut
however, these values can be viewed as probabilities as well. a probability is basically a percentage likelihood expressed as a decimal.
the share for a specific program during a one - hour period is 49.71 while the hut for the same period is 75.09. calculate the rating as a probability for a randomly selected household from all household televisions to be one tuned to the specific program at the specified time.
round to the nearest hundredth (hint: remember it needs to be converted from a percentage to a decimal if looking at probability).

Explanation:

Step1: Identify the formula

We use the formula $Rating = Share\times HUT$.

Step2: Substitute the given values

Given $Share = 49.71$ and $HUT=75.09$, so $Rating=49.71\times75.09$.

Step3: Calculate the product

$49.71\times75.09 = 49.71\times(75 + 0.09)=49.71\times75+49.71\times0.09=(50 - 0.29)\times75+(49.71\times0.09)=(50\times75-0.29\times75)+4.4739=(3750 - 21.75)+4.4739 = 3728.25+4.4739=3732.7239$.

Step4: Convert to probability (decimal)

Since rating is a percentage - like value, to convert to a probability (decimal), we divide by 100. So $P=\frac{3732.7239}{100}=37.327239$.

Step5: Round to the nearest hundredth

Rounding $37.327239$ to the nearest hundredth gives $37.33$.

Answer:

$37.33$