Question

2. Assume that scores on a Dental anxiety scale (ranging from 0 to 20) are normal for the general population, with mean - 11 and standard deviation - 3.5. a) What is the probability that a person chosen at random will score between 10 and 15 on this scale? (0.4859) b) What is the probability that a person chosen at random will have a score larger than 10 on this scale? (0.6125) c) What is the probability that a person chosen at random will have a score less than 5 on this scale? (0.0432)

if can in details so i can understand ?

Answer 1

Given mean (u) = 11 standard deviation (8)= 3.5 find the probability that a person chosen at random will score between 10 and is on this scale. ..pl 10L XC 15) =P ( 10-4 CX-4 (15 ) P OLXc15 (10-11 L24 15-112 -iplloLX(15) =pl-0.2857 L 2C 1.1428) =plz7 -0.2857-P( 271.1428 PlloKXK15) = 0.6124 0.1265 FPLIOS X(15) = 0.4859 1 Lusing the Normal probability integral table] - 0.2857 o 1.1428 too find the probability chosen at random score larger than scale : PLX 710 that will 10 a person. have a on this

:P(X>10) =P ( X-4 >/0-4) - P(x 710) =pl z >10-11) 3 .5 .:Pix710) ap(x710) =P(27-0.2857) - 06/2449 Ž0.6125 PIX>10) = 0.6125 [ using the Normal probability integral table -0.28570 o tig find the probability that a person chosen at random will have a score less than 5 on the scale apl <5) = pl X-u <5-4) =P ( za 5-11) -< 5-11 3.

.pl XC5)=P(24-1.7142) P ( x 5) = 0.0432] [using table Normal probability integral ] co - 1.7142 o