Questions: Hospital visits: According to a health agency, there were 409,706 hospital visits for asthma-related illnesses in a recent year. The age distribution was as follows. Round your answers to four decimal places if necessary. Age Range Number ------ Less than 1 year 7864 1-17 103,045 18-44 79,661 45-64 121,725 65-84 80,655 85 and up 16,756 Total 409,706 Part 1 of 3 (a) What is the probability that an asthma patient is between 65 and 84 years old? The probability that an asthma patient is between 65 and 84 years old is 0.1969. Part 2 of 3 (b) What is the probability that an asthma patient is 85 years old or older? The probability that an asthma patient is 85 years old or older 0.0409. Part 3 of 3 (c) Using a cutoff of 0.05, is it unusual for an asthma patient to be less than 1 year old? Based on a cutoff of 0.05, it is unusual for an asthma patient to be less than 1 year old.

Hospital visits: According to a health agency, there were 409,706 hospital visits for asthma-related illnesses in a recent year. The age distribution was as follows. Round your answers to four decimal places if necessary. Age Range Number ------ Less than 1 year 7864 1-17 103,045 18-44 79,661 45-64 121,725 65-84 80,655 85 and up 16,756 Total 409,706 Part 1 of 3 (a) What is the probability that an asthma patient is between 65 and 84 years old? The probability that an asthma patient is between 65 and 84 years old is 0.1969. Part 2 of 3 (b) What is the probability that an asthma patient is 85 years old or older? The probability that an asthma patient is 85 years old or older 0.0409. Part 3 of 3 (c) Using a cutoff of 0.05, is it unusual for an asthma patient to be less than 1 year old? Based on a cutoff of 0.05, it is unusual for an asthma patient to be less than 1 year old.
Transcript text: Hospital visits: According to a health agency, there were 409,706 hospital visits for asthma-related illnesses in a recent year. The age distribution was as follows. Round your answers to four decimal places if necessary. \begin{tabular}{lr} \hline \multicolumn{1}{r}{ Age Range } & Number \\ \hline Less than 1 year & 7864 \\ $1-17$ & 103,045 \\ $18-44$ & 79,661 \\ $45-64$ & 121,725 \\ $65-84$ & 80,655 \\ 85 and up & 16,756 \\ \hline Total & 409,706 \end{tabular} Part 1 of 3 (a) What is the probability that an asthma patient is between 65 and 84 years old? The probability that an asthma patient is between 65 and 84 years old is 0.1969. Part 2 of 3 (b) What is the probability that an asthma patient is 85 years old or older? The probability that an asthma patient is 85 years old or older 0.0409. Part 3 of 3 (c) Using a cutoff of 0.05, is it unusual for an asthma patient to be less than 1 year old? Based on a cutoff of 0.05, it is unusual for an asthma patient to be less than 1 year old.
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Solution

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Solution Steps

To solve these questions, we need to calculate the probabilities based on the given data. The probability of an event is the number of favorable outcomes divided by the total number of outcomes. For part (c), we compare the calculated probability to the given cutoff to determine if the event is unusual.

Solution Approach
  1. Calculate the probability for each age range by dividing the number of visits in that range by the total number of visits.
  2. For part (c), compare the probability of an asthma patient being less than 1 year old to the cutoff value of 0.05 to determine if it is unusual.
Step 1: Probability of Age 65 to 84

To find the probability that an asthma patient is between 65 and 84 years old, we use the formula:

\[ P(65 \leq \text{age} < 84) = \frac{\text{Number of visits for age 65 to 84}}{\text{Total visits}} = \frac{80655}{409706} \approx 0.1969 \]

Step 2: Probability of Age 85 and Up

Next, we calculate the probability that an asthma patient is 85 years old or older:

\[ P(\text{age} \geq 85) = \frac{\text{Number of visits for age 85 and up}}{\text{Total visits}} = \frac{16756}{409706} \approx 0.0409 \]

Step 3: Probability of Age Less Than 1

We then determine the probability that an asthma patient is less than 1 year old:

\[ P(\text{age} < 1) = \frac{\text{Number of visits for age less than 1}}{\text{Total visits}} = \frac{7864}{409706} \approx 0.0192 \]

Step 4: Unusual Event Determination

To assess whether it is unusual for an asthma patient to be less than 1 year old, we compare the calculated probability to the cutoff of 0.05:

Since \( P(\text{age} < 1) \approx 0.0192 < 0.05 \), we conclude that it is unusual for an asthma patient to be less than 1 year old.

Final Answer

  • The probability that an asthma patient is between 65 and 84 years old is \( \boxed{0.1969} \).
  • The probability that an asthma patient is 85 years old or older is \( \boxed{0.0409} \).
  • It is unusual for an asthma patient to be less than 1 year old: \( \boxed{\text{Yes}} \).
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