Question

stats lesson 2.5 homework name emmalynne here. 1. for a standardized normal distribution, find the area described by each of the following inequalities: a. z < - 0.80 b. - 1.93 < z < 1.38 c. z > 2.26 d. z ≥ 2.26 2. researchers measured the resting heart rate of over 92,000 individuals using wearable devices over a two - year period. the results of the study showed the resting heart rates were approximately normal with a mean of 63 beats per minute (bpm) and a standard deviation of 3.03 bpm. a. what proportion of the individuals in the study have a resting heart rate below 58 bbm? b. what proportion of the individuals in the study have a resting heart rate above 66 bbm? c. what proportion of the individuals in the study have a resting heart rate between 58 and 66 bbm? d. athletes often have lower than average resting heart rates. what is the resting heart rate for an athlete who is at the 10th percentile.

Explanation:

1.

a.

Step1: Use z - table lookup

We know that for a standard - normal distribution, we want to find $P(Z < - 0.80)$. Looking up the value in the standard - normal (z -) table, the value corresponding to $z=-0.80$ is $0.2119$.

Step1: Split the inequality

We know that $P(-1.93 < Z < 1.38)=P(Z < 1.38)-P(Z < - 1.93)$.

Step2: Look up values in z - table

From the z - table, $P(Z < 1.38)=0.9106$ and $P(Z < - 1.93)=0.0268$.

Step3: Calculate the probability

$P(-1.93 < Z < 1.38)=0.9106 - 0.0268=0.8838$.

Step1: Use the property of the total area

We know that $P(Z>2.26)=1 - P(Z < 2.26)$.

Step2: Look up the value in z - table

From the z - table, $P(Z < 2.26)=0.9881$.

Step3: Calculate the probability

$P(Z>2.26)=1 - 0.9881 = 0.0119$.

Answer:

$0.2119$

b.