Question

The distribution of weights of a sample of 500 toddlers is symmetric and bell-shaped.
According to the Empirical Rule, what percent of the weights will lie between plus or
minus three sigmas (standard deviations) from the mean?

Group of answer choices

68%

34%

99.7%

95%

None of these

If a sample of toddlers has an estimated mean weight of 52 pounds and a standard
deviation of 4 pounds, then 95% of the toddlers have weights between which two
values?

If a sample of toddlers has an estimated mean weight of 52 pounds and a standard
deviation of 4 pounds, then what percentage of toddlers weigh between 44 and 56 pounds?

Group of answer choices

68%

34%

None of these

81.5%

47.5%

Group of answer choices

44 pounds and 60 pounds

40 pounds and 64 pounds

48 pounds and 56 pounds

None of these

48 pounds and 60 pounds

Answer 1

1)

99.7%

2)

mena = 52 , s= 4

95% of data falls within 2sd of mean

mena +/- sd
= 52 +/ - 2 *4
= 44 and 60

3)

Here, μ = 52, σ = 4, x1 = 44 and x2 = 56. We need to compute P(44<= X <= 56). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (44 - 52)/4 = -2
z2 = (56 - 52)/4 = 1

Therefore, we get
P(44 <= X <= 56) = P((56 - 52)/4) <= z <= (56 - 52)/4)
= P(-2 <= z <= 1) = P(z <= 1) - P(z <= -2)
= 0.8413 - 0.0228
= 0.8185

81.5%