Question

If x has a normal distribution with mean=146 and standard deviation = 40.86 , find P (100 < x < 146) * 2 points Your answer The life span of CASIO calculators has a normal distribution with average 2 points of 54 months and standard deviation of 8 months. What percentage of calculators will last for at most 36 months? * 98.93% O 1.07% O 1.22% 0 98.78% 100%

Answer 1

Solution:

1)

Given:

$\mu=146$

$\sigma=40.86$

We have to find P(100<X<146) = ...?

Using z-score,

X1 - 21 100 - 146 40.86 = -1.1258 0 X₂ - H 22 146 – 146 40.86 = 0

Therefore,

P(−1.1258 ≤ Z ≤ 0) = P(Z≤0) − P(Z≤−1.1258)

=0.5−0.1301=0.3699 ...Using standard normal table

Hence, P(100<X<146) = 0.3699

2)

Given:

$\mu=54$

$\sigma=8$

We have to find P(X$\leq$ 36) = ..?

Using z-score,

X-H Z= 36 - 54 8 = -2.25 o

Therefore,

P(Z≤−2.25)=0.0122

Hence, P(X$\leq$ 36) = 1.22%

Done