A. Mean and standard deviation.
The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.
The standard deviation of the sampling distribution is:
σₓ̄ = σ / √n
Plugging in values:
σₓ̄ = 6.9 / √25 = 1.38
b. Calculate z-scores for both values:
z = (value - mean) / standard deviation
For 172.5:
z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068
For 175.8:
z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83
The difference between these probabilities is 0.762.
Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.
c. Z-score for 172 cm:
z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03
Hence, samples with means below 172 cm equal 0.03 × 200 = 6.
Answer: 12 days
Step-by-step explanation:
Distance = speed x time
2214.50 = 21.14 / t
t = 2214.50 / 21.14 = 104.75 hours
By cycling 9 hours each day, it will take
104.75 / 9 = 11.64 = 12 days
The task requires calculating the coefficient of the squared term in the parabolic equation, and based on my calculations and analysis, I found that the vertex of the parabola can be expressed as y =a(x-h)^2+k, leading me to a simplification that results in x^2.
