Question

Find the probability that a piece of data from a standard normal distribution will have a standard score described by the following: ot na a) Less than z = 1.25 b) Between 2 = -2.03 and z= -0.69 soy blue V c) Find the score associated with the 62nd percentile ODE Venom ONO

Answer 1

1).a).$\mathbf{P(Z<1.25)}$

= Φ(1.25)

$\approx\mathbf{0.8944}$ [ using normal table]

b).$\mathbf{P(-2.03<Z<-0.69)}$

= P(Z < -0.69) - P(Z < -2.03)

$=\Phi(-0.69)-\Phi(-2.03)$

=1 – Φ(0.69) – 1+ Φ(2.03)

= -Φ(0.69) + Φ(2.03)

$=-0.7549+0.9788$ [ using normal table]

$=\mathbf{0.2239}$

c).let z be the 62nd percentile.

$P(Z\leq z)=0.62$

+ Φο) = 0.62

$\Rightarrow z=\Phi^{-1}(0.62)$

=z=0.3055 0.31

the score for 62nd percentile = 0.31

2).the given data are:-

margin of error (E) = 2% = 0.02

proportion (p) = 0.12

z critical value for 92% confidence level, both tailed test be:-

$z^*=1.751$ [ in excel type =NORMSINV(0.96)]

the needed sample size be:-

$=\left ( \frac{z^*}{E} \right )^2*p*(1-p)$

$=\left ( \frac{1.751}{0.02} \right )^2*0.12*(1-0.12)$

$\approx\mathbf{810}$

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