Question

The overhead reach distances of adult females are normally distributed with a mean of 204 and a standard deviation of 8.5 cm. Round to four decimal places

A. Find the probability that the individual distance is greater than 216

B. With a mean of 204 and a standard deviation of 8.5 cm. Find the probability if 23 randomly selected distances is greater than 202 cm.

Please show work thank you

Answer 1

  Solution :

Given that ,

a.

mean = = 204

standard deviation = = 8.5

P(x >216 ) = 1 - P(x <216 )

= 1 - P[(x - ) / < (216-204) / 8.5]

= 1 - P(z < 1.41)

Using z table,

= 1 -0.9207

=0.0793

b.

mean = = 204

standard deviation = = 8.5

n =

= 204

= / n = 8.5 / 23 = 1.77

P( > 202) = 1 - P( < 202)

= 1 - P[( - ) / < (202-204) / 1.77]

= 1 - P(z < -1.13)

Using z table,    

= 1 - 0.1292

= 0.8708