The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation o

Question

3 years ago

15

The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation o

f time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less

Mathematics

1 answer:

faust18 [17] · Answer 1 · 2022-07-01T15:11:39+03:00

faust18 [17]3 years ago

6 0

Answer:

required probability is 0.8413

Step-by-step explanation: Given mean $\mu =15$ minutes, standard deviation $\sigma =4$ seconds, we need to find $P\left ( X\leq 19 \right )$ . Using z score

$z=\frac{X-\mu }{\sigma }\\=\frac{19-15}{4}\\=1$

So,

$P\left ( X\leq 19 \right )\\=P\left ( Z\leq 1 \right )\\=0.8413$