Question

A tech company’s average daily stock price last year was $38.12, with a standard deviation of $2.45. If a random selection of 32 days were chosen from last year, what is the probability that the average price of the company’s stock for those 32 days is more than $37.00?

Multiple Choice

0.9295

0.9529

0.9952

0.9259

Answer 1

Given,

$\mu$ = 38.12, $\sigma$ = 2.45

The central limit theorem is

P( $\bar{x }$ < x) = P( Z < x - $\mu$ / $\sigma$ / sqrt(n) )

So,

P( $\bar{x }$ > 37) = P( Z > 37 - 38.12 / 2.45 / sqrt(32) )

= P( Z > -2.59)

= P( Z < 2.59)

= 0.9952