Question

The mark obtainable in an English test by a students are 1,2,3,4….20 Points according to how they perform . The mean mark is 13.5 He standard deviation is 2.4 The mark is normally distributed find the maximum mark of the lowest 10% of the class

Answer 1

To find the maximum mark of the lowest 10%, a z-score corresponding to the 10th percentile is used with the mean and standard deviation. The z-score -1.28 applied to the normal distribution with given values results in 10.428, which we round down to the nearest whole number to get a maximum mark of 10.

Step-by-step explanation:

To find the maximum mark of the lowest 10% of the class, given that the marks are normally distributed, with a mean of 13.5 and a standard deviation of 2.4, we need to use a z-score table to find the z-score corresponding to the 10th percentile.

The 10th percentile z-score is approximately -1.28. We can then use the z-score formula:

Z = (X - μ) / σ

Where Z is the z-score, X is the value in the dataset, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for X gives us:

X = Z×σ + μ

Now, we plug in the values:

X = (-1.28)×(2.4) + 13.5

X = -3.072 + 13.5 = 10.428

Since marks cannot be fractional, we can say that the maximum mark for the lowest 10% is 10.