Question

Suppose data set X has mean μ = 400 and standard deviation σ = 50. If a random sample
of size 100 is collected and ̄x is the sample mean, compute P(395 ≤ x ̄ ≤ 410).

Answer 1

Solution :

Given that,

mean = = 400

standard deviation = = 50

n = 100

= 400

₌ / n = 50 100 = 5

P( 395 ≤ ≤ 410 )

P (395- 400 / 5 ) ≤ ( - / ) ≤ ( 410 - 400 / 5)

P ( - 5 / 5 ≤ z ≤ 10 / 5 )

P (-1 ≤ z ≤ 2 )

P ( z ≤ 2 ) - P ( z ≤ -1 )

Using z table

= 0.9772 - 0.1587

= 0.8185

Probability = 0.8185