Explanation

KE = 1/2mv²

Given m = 0.03 kg, v = 400 m/s

KE = 1/2 × 0.03 × 400 × 400

= 1/2 × 0.03 × 160000

= 1/2 × 4800

= 2400 J

Explanation

Step 1: Calculate the mean of the marks.

Mean = (6 + 8 + 10 + 12 + 4 + 20) / 6

= 60 / 6

= 10

Step 2: Calculate the mean deviation.

Mean Deviation = (|6-10| + |8-10| + |10-10| + |12-10| + |4-10| + |20-10|) / 6

= (4 + 2 + 0 + 2 + 6 + 10) / 6

= 24 / 6

= 4

Step 3: Calculate the coefficient of dispersion.

Coefficient of Dispersion = Mean Deviation / Mean

= 4 / 10

= 0.4

Explanation

The standard deviation of a binomial distribution is indeed √npq, where:

• n is the number of trials
• p is the probability of success
• q is the probability of failure (q = 1 - p)

The formula for the standard deviation of a binomial distribution is:

σ = √npq

This represents the spread or dispersion of the distribution.

Explanation

Geometric Mean = ∛(2 × 4 × 8)

= ∛64

= 4

Explanation

A bimodal distribution has two modes, meaning two values occur with the highest and equal frequency.

It indicates the presence of two peaks in the data set.

Explanation

A small standard deviation means the data is tightly clustered around the mean.

This results in a less spread out (narrower) normal distribution curve.

Explanation

Mode is the value that occurs most frequently in a dataset.

It represents the most common or popular item in the data.

Explanation

To find the range, subtract the smallest value from the largest value:

Maximum value = 28

Minimum value = 20

Range = Maximum value - Minimum value

= 28 - 20

= 8

Explanation

Identify the given values: The sum of observations is Sum=1500

. The number of observations is n=30 

Average = Sum of observations / Number of observations

= 1500 / 30

= 50

Explanation

Median is the middle value when data is arranged in order.

Ordered data: 63, 65, 66, 67, 69 → middle value is 66.