Question

669

If the duration of heart disease from the onset of symptoms until death ranges from 2 to 29 years, the average is 8.5 years with a standard deviation of 4 years. One nurse of a public medical center randomly selected the medical records of 30 deceased patients from the medical center’s database and records the average duration.

Find the probability for :

1. the average duration is less than 6 years.

2. the average duration exceeds 7 years.

3. the average duration is between 7.4 and 9.4 years.

Answer 1

u = 8.5, = 4

we have,

z = (x-u)/

1. P(the average duration is less than 6 years)

= P(x < 6)

= P(z < (6-8.5)/4)

= P(z < -0.625)

= 0.2660

2. the average duration exceeds 7 years.

= P(x > 7)

= P(z > (7-8.5)/4)

= P(z > -0.375)

= 0.6462

3. the average duration is between 7.4 and 9.4 years.

= P(7.4 < x < 9.4)

= P((7.4-8.5)/4 < z < ((9.4-8.5)/4)

= P(-0.275 < z < 0.225)

= P(z < 0.225) - P(z < -0.275)

=0.5890 - 0.3917

= 0.1973