The infant mortality rate (per 1,000 live births) for the 50 states and the District of Columbia has a mean of 6.98 and a standard deviation of 1.62. Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births)? |
answer)
As the given data is normally distributed
We can use standard normal z table to estimate the answer
Given mean = 6.98
S.d = 1.62
Z = (x-mean)/s.d
We need to find
P(5.36<x<8.60) = p(x<8.6) - p(x<5.36)
P(x<8.6)
Z = (8.6 - 6.98)/1.62
Z = 1
From z table, p(z<1) = 0.8413
P(x<5.36)
Z = (5.36 - 6.98)/1.62
Z = -1
From z table
P(z<-1) = 0.1587
Required proportion is
0.8413 - 0.1587
= 0.6826
That is 68.26%
Or approximately 68%
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