Question

The blood platelet counts of a random sample of 873 women have a normal distribution with a mean of 253.1 and a standard deviation of 62.7 (all units are in 1,000 cells per microliter). Use the empirical rule to find the approximate percentage of women with platelet counts between 127.7 and 378.5. Enter a percentage as an integer or a decimal; do not round and do not include a"%".

The approximate percentage of women with platelet counts between 127.7 and 378.5 is [PlateletEmp] percent.

Answer 1

The approximate percentage of women with platelet counts between 127.7 and 378.5

P( 127.7 ≤x≤378.5) = 0.9544 or 95 percentage

Explanation:

Step(i):-

Mean of the Population = 253.1

Given standard deviation of the Population = 62.7

Given sample size 'n' = 873

Let 'X' be the random variable in Normal distribution

Let x₁ = 127.7

`Z_(1) = (x_(1) -mean)/(S.D) = (127.7-253.1)/(62.7) = -2`

Let x₂ = 378.5

`Z_(2) = (x_(2) -mean)/(S.D) = (378.5-253.1)/(62.7) = 2`

Step(ii):-

The probability of women with platelet counts between 127.7 and 378.5.

P( 127.7 ≤x≤378.5) = P( -2≤Z≤2)

= P(Z≤2) - P(Z≤-2)

= 0.5 +A(2) - ( 0.5 - A(-2))

= A(2) + A(2) (∵A(-2) =A(2)

= 2 × A(2)

= 2× 0.4772

= 0.9544

Conclusion:-

The approximate percentage of women with platelet counts between 127.7 and 378.5 is 0.9544 or 95 percentage