The weight of certain population of young females is approximately normally distributed with the mean of 66 kg and a standard deviation of 7.5 kg. If an individual is selected at random from this population, find the probability that she will weigh more than 77.5 kg.
To find the probability that a randomly selected individual will weigh more than 77.5 kg, we need to calculate the area under the normal distribution curve to the right of 77.5 kg.
To do this, we can use the standard normal distribution by converting the weight of 77.5 kg to a z-score.
The z-score formula is:
z = (x - μ) / σ
where x is the individual weight, μ is the mean weight, and σ is the standard deviation.
Plugging in the values:
z = (77.5 - 66) / 7.5
z = 11.5 / 7.5
z ≈ 1.533
Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 1.533.
Using a standard normal distribution table, the probability corresponding to a z-score of 1.533 is approximately 0.9382.
Therefore, the probability that a randomly selected individual will weigh more than 77.5 kg is approximately 0.9382 or 93.82%.
To find the probability that a randomly selected individual from this population will weigh more than 77.5 kg, we can use the standard normal distribution.
First, we need to standardize the value of 77.5 kg using the z-score formula:
z = (x - μ) / σ
where:
- x is the value we want to standardize (77.5 kg)
- μ is the mean of the population (66 kg)
- σ is the standard deviation of the population (7.5 kg)
Let's plug in the values:
z = (77.5 - 66) / 7.5
z = 11.5 / 7.5
Now, we can use a Z-table or a calculator to find the probability associated with this z-score.
Using a Z-table, we can find that the probability of obtaining a z-score greater than 1.53 (rounded to two decimal places) is approximately 0.063.
Therefore, the probability that a randomly selected individual from this population will weigh more than 77.5 kg is approximately 0.063 or 6.3%.
To find the probability that a randomly selected individual from the population will weigh more than 77.5 kg, we need to use the z-score formula and the standard normal distribution.
The z-score formula is given by:
z = (x - μ) / σ
Where:
- x is the value we are interested in (77.5 kg in this case)
- μ is the mean of the population (66 kg in this case)
- σ is the standard deviation of the population (7.5 kg in this case)
Let's calculate the z-score first:
z = (77.5 - 66) / 7.5
z = 11.5 / 7.5
z ≈ 1.53
The z-score tells us how many standard deviations above or below the mean a value is. In this case, 77.5 kg is approximately 1.53 standard deviations above the mean.
Next, we need to find the probability corresponding to this z-score using a standard normal distribution table or a calculator. The table or calculator will give us the probability of finding a value to the right of the given z-score.
Using a standard normal distribution table or calculator, we find that the probability (area under the curve) to the right of a z-score of 1.53 is approximately 0.0630.
Therefore, the probability that a randomly selected individual from this population will weigh more than 77.5 kg is approximately 0.0630, or 6.30%.