A movie studio surveyed married couples about the types of movies they prefer.In the survey, the husband and wife were each asked if they prefer action, comedy, or drama.Here is a summary of the data the studio got after asking 75 couples.Husband Wife Number of couplesaction action 8action comedy 5action drama 12comedy action 6comedy comedy 9comedy drama 8drama action 7drama comedy 9drama drama 11Suppose the movie studio will ask 100 more couples about their movie preferences.How many of these 100 couples will have at most one spouse prefer comedy movies? Use the data to make a prediction.
Question
A movie studio surveyed married couples about the types of movies they prefer.In the survey, the husband and wife were each asked if they prefer action, comedy, or drama.Here is a summary of the data the studio got after asking 75 couples.Husband Wife Number of couplesaction action 8action comedy 5action drama 12comedy action 6comedy comedy 9comedy drama 8drama action 7drama comedy 9drama drama 11Suppose the movie studio will ask 100 more couples about their movie preferences.How many of these 100 couples will have at most one spouse prefer comedy movies? Use the data to make a prediction.
Solution 1
To predict the number of couples where at most one spouse prefers comedy movies, we first need to identify the categories from the survey data where at most one spouse prefers comedy. These categories are:
- Husband prefers action, wife prefers action: 8 couples
- Husband prefers action, wife prefers drama: 12 couples
- Husband prefers comedy, wife prefers action: 6 couples
- Husband prefers drama, wife prefers action: 7 couples
- Husband prefers drama, wife prefers drama: 11 couples
Adding these numbers together, we find that 44 out of 75 surveyed couples have at most one spouse who prefers comedy movies.
To predict how many out of 100 more couples will have at most one spouse prefer comedy movies, we can set up a proportion:
44/75 = x/100
Solving for x gives us the predicted number of couples. Multiply each side by 100 to get:
x = (44/75) * 100 = 58.67
Since we can't have a fraction of a couple, we round to the nearest whole number. Therefore, we predict that approximately 59 out of the next 100 couples surveyed will have at most one spouse who prefers comedy movies.
Solution 2
To predict the number of couples where at most one spouse prefers comedy movies, we first need to identify the categories from the survey data that fit this criteria. These categories are:
- Husband prefers action, wife prefers action: 8 couples
- Husband prefers action, wife prefers drama: 12 couples
- Husband prefers comedy, wife prefers action: 6 couples
- Husband prefers comedy, wife prefers drama: 8 couples
- Husband prefers drama, wife prefers action: 7 couples
- Husband prefers drama, wife prefers drama: 11 couples
Adding these numbers together, we find that 52 out of the 75 surveyed couples fit this criteria.
To predict how many out of the next 100 couples will fit the same criteria, we can use the proportion from the survey data. The proportion is 52/75, which is approximately 0.6933.
Multiplying this proportion by 100 gives us the predicted number of couples: 0.6933 * 100 = 69.33.
Since we can't have a fraction of a couple, we round this to the nearest whole number. Therefore, we predict that approximately 69 out of the next 100 couples will have at most one spouse who prefers comedy movies.
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