The time spent (in days) waiting for a heart transplant in two states for patien

Question

The time spent (in days) waiting for a heart transplant in two states for patients with type A the right. Complete parts (a) and (oj below. blood can be approximated by a nomal distribution, as shown in the graph to c-188 (a) What is the shortest time spent waiting for a heart that would still place a patient in the top 10% of waiting times? days (Round to two decimal places as needed.) (b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 10% of waitng times? days (Round to two decimal places as needed.) The total chalesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 201 miligrams per decilder and a slandard devatian of 37 7 millgrams per decilite (a) What percent of the men have a total cholesterol level less than 234 milligrams per deciliter of blood? h) If 249 men in the 35 44 age group are randomly selecled, about haw many would you expect to have a total chalesterol lavel greater than 262 milligrams per deciliter of blood? % a) The percent of the men that have a total cholesterol level less than 234 milligrams per deciliter of blood is Round to two decimal places as needed.) b) Of the 249 men seleedwould be expected to have a tolal cholesteral level greater than 262 miligrams per decileof bicod Round to the nearest integer as needed.) The maan incubation time for a type of fertilized egg kept at 100.5'F is 23 days. Suppose that the incubation times are approximatey normally distributed with a standard deviation of 1 day less than 22 days? (a) What is the pr b) What is the probability that a ramly selected fartilized egg hatches betasen 21 and 23 days? (c) What is the probability that a randomly selected fertized egg takes over 24 days to hatch? thal a randomly selected fertilized egg hatches i a) The probability that a randomly selecled ferblized egg halches in less than 22 days is Round to four decimal places as needed.) (b) The probability that a randomly selected fentlized egg hatches between 21 and 23 days is Round to four decimal places as needed.) (c) The probability that a randomly selected fertilized egg takes over 24 days to hatch is Round to four decimal places as needed.) Assume the random variable x is normally distributed with mean -85 and standard deviation o = 5, Find the indicated probability P(x

Explanation / Answer

SD = 18.8

looking up a z- table q1

We know the percentage we are trying to find, the top 10% of patients, corresponds to 0.9. As such, we first need to find the value 0.9 in standard normal distribution table.

=>When we go to the table, we find that the value 0.90 is not there exactly, however, the values 0.8997 and 0.9015 are there and correspond to Z values of 1.28 and 1.29, respectively

shortest time for top 10% waiting = mean + 1.28*SD
= 125 + 18.8*1.28

= 147 days (approx)

q2
z-value for bottom 1% waiting time = - 2.3263
longest time for bottom 1% waiting = mean - 2.3263*SD
= 125 - 18.8*2.3263
= 81 days

(a) x1 = 234; = 201; = 37.7
z = ( x1 - ) / = 0.8753
P (x < 234) = P (z < 0.8753) = 0.6315

(b) x1 = 262; = 201; = 37.7; = 249; (÷) = 2.3889
z = ( x1 - ) / (÷) = 61/2.39 = 25.53
P (262 < x) = P (25.53 < z) = 0

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