select the correct answer from the drop - down menu.\nthe mean midday temperature recorded in june in a city…
select the correct answer from the drop - down menu.\nthe mean midday temperature recorded in june in a city in south california is 36°c, and the standard deviation is 3°c. the number of days in the month of june is 30.\nassuming the data is normally distributed, the number of days in june when the midday temperature was between 39°c and 42°c is
Answer
Explanation:
Step1: Calculate z - scores
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 39^{\circ}C$, $\mu=36^{\circ}C$, and $\sigma = 3^{\circ}C$, $z_1=\frac{39 - 36}{3}=\frac{3}{3}=1$. For $x = 42^{\circ}C$, $\mu = 36^{\circ}C$, and $\sigma=3^{\circ}C$, $z_2=\frac{42 - 36}{3}=\frac{6}{3}=2$.
Step2: Find the probability
Using the standard normal distribution table, the probability corresponding to $z = 1$ is $P(Z < 1)=0.8413$ and the probability corresponding to $z = 2$ is $P(Z < 2)=0.9772$. The probability that $1<Z<2$ is $P(1 < Z < 2)=P(Z < 2)-P(Z < 1)=0.9772 - 0.8413=0.1359$.
Step3: Calculate the number of days
The number of days in June is $n = 30$. The number of days with temperature between $39^{\circ}C$ and $42^{\circ}C$ is $n\times P(1 < Z < 2)=30\times0.1359\approx4$.
Answer:
4