Did I calculate this correctly? Thank you. ### Confidence Intervals for Heartbeat Rates#### Problem Statement:We wish to estimate the average number of heartbeats per minute for a certain population. The average number of heartbeats per minute for a sample of 49 subjects was found to be 90. Assume that these 49 patients constitute a random sample, and that the population is normally distributed with a standard deviation of 10.#### Task:Find the 90%, 95%, and 99% confidence intervals for the mean number of heartbeats per minute for a certain population.#### Data Provided:- Sample size (\( n \)) = 49- Standard deviation (\( \sigma \)) = 10- Sample mean (\( \bar{X} \)) = 90- Critical values for Z at different confidence levels: - \( Z_{c \, 90\%} = 1.645 \) - \( Z_{c \, 95\%} = 1.96 \) - \( Z_{c \, 99\%} = 2.575 \)#### Formulas:The formula to calculate the confidence interval is given by:\[ \bar{X} \pm Z_{c} \left( \frac{\sigma}{\sqrt{n}} \right) \]#### Calculations:1. **90% Confidence Interval:** \[ 90 \pm 1.645 \left( \frac{10}{\sqrt{49}} \right) \] Simplified: \[ 90 \pm 1.645 \left( \frac{10}{7} \right) \] \[ 90 \pm 1.645 \times 1.4286 \approx 90 \pm 2.35 \] **90% Confidence Interval:** \( (87.65, 92.35) \)2. **95% Confidence Interval:** \[ 90 \pm 1.96 \left( \frac{10}{\sqrt{49}} \right) \] Simplified: \[ 90 \pm 1.96 \left( \frac{10}{7} \right) \] \[ 90 \pm 1.96 \times 1.4286 \approx 90 \pm 2.8

Name: Did I calculate this correctly? Thank you. ### Confidence Intervals fo
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Did I calculate this correctly? Thank you. ### Confidence Intervals for Heartbeat Rates#### Problem Statement:We wish to estimate the average number of heartbeats per minute for a certain population. The average number of heartbeats per minute for a