Question

The infant mortality rate (per 1,000 live births) for the 50 states and the District of...

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)?

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Answer #1

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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