In a distribution exactly normal with mean 47.5 Kilogram, 89.97% of the items are under 70 kilogram weight. Then which of the following is the standard deviation of the distribution? Given that area under standard normal curve from Z=0 to Z=1.28 is 0.3997.
Question
In a distribution exactly normal with mean 47.5 Kilogram, 89.97% of the items are under 70 kilogram weight. Then which of the following is the standard deviation of the distribution? Given that area under standard normal curve from Z=0 to Z=1.28 is 0.3997.
Solution
To solve this problem, we need to use the properties of a normal distribution.
-
First, we know that the mean (μ) of the distribution is 47.5 kg.
-
We also know that 89.97% of the items are under 70 kg. In terms of a standard normal distribution, this corresponds to a Z-score of 1.28 (since the area under the standard normal curve from Z=0 to Z=1.28 is 0.3997, and 0.5 (from Z=0 to Z=-∞) + 0.3997 = 0.8997 or 89.97%).
-
The Z-score is calculated using the formula Z = (X - μ) / σ, where X is the value from the original distribution, μ is the mean, and σ is the standard deviation.
-
We can plug in the values we know: 1.28 = (70 - 47.5) / σ.
-
Solving for σ, we get σ = (70 - 47.5) / 1.28 = 17.578125 kg.
So, the standard deviation of the distribution is approximately 17.58 kg.
Similar Questions
The mean weight of 1000 students at a certain college is 62 kg, and the standard deviation is 5kg. Assuming that the weights are normally distributed, find the probability that a randomly selected student weighs between 55 and 60kg.a.0.3446b.0.0808c.0.2638d.0.7362
A miniature American Eskimo dog has a mean weight of 15 pounds with a standard deviation of 2 pounds. Assuming the weights of miniature Eskimo dogs are normally distributed, what range of weights would 68% of the dogs have? (1 point)Approximately 13–17 poundsApproximately 14–16 poundsApproximately 11–19 poundsApproximately 9–21 pounds
Parcels of printed matter being posted from the office are always weighted. The weights have been found to be normally distributed with a mean of 8.35kg and a standard deviation of 2.25kg.Find the proportion of parcels whose weights are (i) less than 10kg (Give answer correct to 3 decimal places) (ii) between 6.5kg and 9kg. (Give answer correct to 3 decimal places) (iii) What weight would a parcel need to be to be in the top 15% of weights? (Give answer correct to 2 decimal places)
In a normal distribution, how much of the data falls within one standard deviation?99.7%95%100%68%
What is the probability that a normally distributed random variable lies within 1.65 standard deviations of the mean?Note: You can use the Z table here.95%90%85%80%
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.