State the conditions under which the normal distribution may be used as an approximation to the binomial distribution.

A manufacturer of electric components claims that 45% of their batch of sensors are high-precision.

Explain why the company should not test every sensor produced to verify this claim.

To test the manufacturer's claim, a random sample of 300 sensors was tested.

State the hypotheses for a two-tailed test of the company’s claim.

Given that 150 of the 300 sensors were found to be high-precision,

use a normal approximation to test, at the 10% level of significance, whether or not the manufacturer's claim is justified.