Question

the b one

The length of sweet pea flower stems are normally distributed with mean 18.2 cm and standard deviation 2.3 cm. a. Find the probability that the length of a flower stem is between 16 cm and 20 cm b.Stem lengths less than 14 cm and more than 24 cm are unacceptable at a florist's shop. In a batch of 500 sweetpea estimate how many would be unacceptable! Poin 40

Answer 1

μ = 18.2

σ = 2.3

z = x - μ / σ

A)

P( 16 < X < 20)

= P(16 - 18.2/2.3 < Z < 20-18.2/2.3 )

= P(-0.96 < Z < 0.78)

= 0.3315 + 0.2823 [STANDARD NORMAL DISTRIBUTION TABLE]

= 0.6138

B)

Unacceptable sweetpeas  probabality

=P(X < 14) + P(X >24)

= P(Z < 14 - 18.2/2.3) + P(Z > 24-18.2/2.3)

= P(Z < -1.83) + P(Z > 2.52)

= (0.5-0.4664) + (0.5-0.4941)

= 0.0395

Number of sweetpeas are unacceptable

= 500 x 0.0395

= 19.75

=20