Answer:
a. The sample size is approximately 97 adults
Step-by-step explanation:
The given parameters are;
The number of adults surveyed, n = 174
The lowest value of the pulse rate = 39 bpm
The highest value of the pulse rate = 111 bpm
The level of confidence used for determining the sample size = 90%
The given sample mean = 3 pm of the population mean
a. The range rule of thumb states that the standard deviation is approximately one quarter (1/4) of the range
The range = 111 bpm - 39 bpm = 72 bpm
Therefore, the standard deviation, σ = 72 bpm/4 = 18 bpm
The sample size, 'N', is given as follows;
![N = \dfrac{z^2 \cdot p \cdot q}{e^2}](https://tex.z-dn.net/?f=N%20%3D%20%5Cdfrac%7Bz%5E2%20%5Ccdot%20p%20%5Ccdot%20q%7D%7Be%5E2%7D)
Where;
N = The sample size
z = The confidence level, 90% (z-score at 90% = 1.645)
p·q = σ² = 18² = 324
e² = 3² = 9
![N = \dfrac{1.645^2 \times 324}{3^2} = 97.4169](https://tex.z-dn.net/?f=N%20%3D%20%5Cdfrac%7B1.645%5E2%20%20%5Ctimes%20324%7D%7B3%5E2%7D%20%3D%2097.4169)
Therefore the appropriate sample size, N ≈ 97 adults.