In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Homework Help:
4VA. Calculating normal probabilities (2:18)
4DF. Probabilities from Normal Distributions 3 (DOCX)
$-0.19$
0.62
0.19
0.81
Answer
The probability that a randomly selected individual would spend between 35 and 48 minutes on the treadmill is approximately \(\boxed{0.815}\).
Step 1 ：Given values are mean = 42.5, standard deviation = 4.8, x1 = 35 and x2 = 48.
Step 2 ：Standardize the values by subtracting the mean from each value and dividing by the standard deviation. This gives z1 = -1.5625 and z2 = 1.1458333333333335.
Step 3 ：Find the probabilities associated with these z-scores using the cumulative distribution function for a normal distribution. This gives prob1 = 0.05908512293266755 and prob2 = 0.8740679399933936.
Step 4 ：Find the probability of the range by subtracting prob1 from prob2. This gives prob_range = 0.8149828170607261.
Step 5 ：The probability that a randomly selected individual would spend between 35 and 48 minutes on the treadmill is approximately \(\boxed{0.815}\).
