Question

Find the following probabilities for X = pulse rates of group of people, for which the mean is 76 and the standard deviation is 8. Assume a normal distribution. (Round all answers to four decimal places.)

(a) P(X ≤ 70).

(b) P(X ≥ 86).

(c) P(56 ≤ X ≤ 92).

Answer 1

Solution :

Given that ,

mean =   = 76

standard deviation = = 8

P(x  70)

= P[(x - ) /   (70-76) / 8]

= P(z -0.75 )

Using z table,

=0.2266

probability=0.2266

(B)

P(x ≥ 86 ) = 1 - P(x86 )

= 1 - P[(x -) / < (86-76) / 8 ]

= 1 - P(z1.25 )

Using z table

= 1 - 0.8944

= 0.1056

probability=0.1056

(C)

P(56 ≤ X ≤ 92)

= P[( 56-76/ 8) (x - ) / ( 92-76/ 8) ]

= P( -2.5 z 2)

= P(z 2 ) - P(z -2.5)

Using z table,   

=0.9772-0.0062

=0.9710

probability=0.9710