Chebyshev's inequality is:
P(|X-μ)≥kσ)≤1/k2, where μ=mean and σ=standard deviation. σ2 is the variance. This means the probability that the data lie at least (or more than) k standard deviations from the mean does not exceed 1/k2.
This can also be stated:
P(|X-μ)≤kσ)≥1-1/k2. This means the probability that the data are within k standard deviations of the mean is at least 1-1/k2.
(a) Given that P≥50%, P≥0.5 for at least 50% of the scores to be within k standard deviations (10k) from the mean 70, then:
0.5=1-1/k2, 1/k2=0.5, 1=0.5k2, 2=k2, k=√2 (about 1.41).
(b) Given that P≤10%, P≤0.1 for at most 10% of the scores to be within k standard deviations of the mean, then:
0.1=1/k2, 0.1k2=1, k2=10, k=√10 (about 3.16).